Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan

Image reconstruction from truncated fan-beam projections along a circular trajectory using the virtual fan-beam method

Objective.In this paper, we investigate how the virtual fan-beam (VFB) method can be used to perform mathematically correct 2D reconstruction in a region-of-interest (ROI), using truncated fan-beam projections acquired on a circular scan, for truncation that only occurs on one side of the object.Approach.We start by choosing a virtual fan-beam trajectory and specifying how to obtain the corresponding virtual projections. Then, three VFB formulas are obtained by applying known super-short-scan (SSS) formulas to this virtual trajectory. Two of them perform the backprojection in a virtual parallel geometry and the third in the virtual fan-beam geometry. Next, we develop two VFB formulas that perform the backprojection step in the fan-beam acquisition geometry.Main results.We present five VFB reconstruction formulas for this truncation setting. To our knowledge, the two VFB formulas performing the backprojection in the fan-beam acquisition geometry are new. Moreover, the five VFB formulas presented here obtain accurate reconstruction in a larger ROI than what has been previously reported in the literature in the same setting. A complete mathematical derivation of these five VFB formulas is given, and their implementation is described step by step. Numerical simulations, using the Forbild head and thorax phantoms, demonstrate the efficacy of these formulas. A spatial resolution analysis and a variance study indicate minor differences between these five VFB formulas.Significance.This work shows that many different VFB formulas can be applied to perform mathematically correct 2D reconstruction in a ROI, in case of truncated fan-beam projections acquired on a circular scan. Moreover, the two new VFB formulas, with backprojection in the acquisition geometry, may open the path for an extension of the VFB method to 3D reconstruction from transversely truncated cone-beam projection acquired on a circular scan.

SHCT: segmented helical computed tomography based on multiple slant source-translation

Micro-computed tomography (Micro-CT) is inevitably required to inspect long large objects with high resolution. It is well known that helical CT solves the so-called "long object" problem, but it requires that the measured object be strictly located in the lateral field of view (FOV). Therefore, developing a novel scanning method to extend the FOV in both the lateral and axial directions (i.e., the large helical FOV) is necessary. Recently, due to the application of linearly distributed source arrays and the characteristics of easy extension of the FOV and engineering implementation, straight-line scanning systems have attracted much attention. In this paper, we propose a segmented helical computed tomography (SHCT) based on multiple slant source-translation. SHCT can readily extend the helical FOV by adjusting the source slant translation (SST) length, pitch (or elevation of the SST trajectory), and number of scanning circles. In SHCT, each projection view is truncated laterally and axially, but the projection data set within the cylindrical FOV region is complete. To ensure reconstruction efficiency and avoid the lateral truncation, we propose a generalized backprojection-filtration (G-BPF) algorithm for SHCT approximate reconstruction. Experimental results verify the effectiveness of the proposed SHCT methods for imaging large and long objects. As the pitch decreases, the proposed SHCT methods can reconstruct competitive, high-quality volumes.

Generalized-equiangular geometry CT: Concept and shift-invariant FBP algorithms

BACKGROUND

With advanced x-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an x-ray source might be positioned radially far away from the focus of arced detector array that is equiangularly spaced, is of importance in many novel CT systems and designs.

PURPOSE

GEGCT, unfortunately, has no theoretically exact and shift-invariant analytical image reconstruction algorithm in general. In this study, to obtain fast and accurate reconstruction from GEGCT and to promote its system design and optimization, an in-depth investigation on a group of approximate Filtered Back-Projection (FBP) algorithms with a variety of weighting strategies has been conducted.

METHODS

The architecture of GEGCT is first presented and characterized by using a normalized-radial-offset distance (NROD). Next, shift-invariant weighted FBP-type algorithms are derived in a unified framework, with pre-filtering, filtering, and post-filtering weights, for both fixed and dynamic NROD configurations. Three viable weighting strategies are then presented including a classic one developed by Besson in the literature and two new ones generated from a curvature fitting and from an empirical formula, where all of the three weights can be expressed as certain functions of NROD. After that, an analysis of reconstruction accuracy is conducted with a wide range of NROD. Finally, the weighted FBP algorithm for GEGCT is extended to a three-dimensional form in the case of cone-beam scan with a cylindrical detector array.

RESULTS

Theoretical analysis and numerical study show that weights in the shift-invariant FBP algorithms can guarantee highly accurate reconstruction for GEGCT. A simulation of Shepp-Logan phantom and a GEGCT scan of lung mimicked by using a clinical lung CT dataset both demonstrate that FBP reconstructions with Besson and polynomial weights can achieve excellent image quality, with Peak Signal to Noise Ratio and Structural Similarity being at the same level as that from the standard equiangular fan-beam CT scan. Reconstruction of a cylinder object with multiple contrasts from simulated GEGCT scan with dynamic NROD is also highly consistent with fixed ones when using the Besson and polynomial weights, with root mean square error less than 7 hounsfield units, demonstrating the robustness and flexibility of the presented FBP algorithms. In terms of resolution, the direct FBP methods for GEGCT could achieve 1.35 lp/mm of spatial resolution at 10% modulation transfer functions point, higher than that of the rebinning method which can only reach 1.14 lp/mm. Moreover, 3D reconstructions of a disc phantom reveal that a greater value of NROD for GEGCT will bring less cone beam artifacts as expected.

CONCLUSIONS

We propose the concept of GEGCT and investigate the feasibility of using shift-invariant weighted FBP-type algorithms for reconstruction from GEGCT data without rebinning. A comprehensive analysis and phantom studies have been conducted to validate the effectiveness of proposed weighting strategies in a wide range of NROD for GEGCT with fixed and dynamic NROD.

Implementation and experimental evaluation of Mega-voltage fan-beam CT using a linear accelerator

BACKGROUND

Mega-voltage fan-beam Computed Tomography (MV-FBCT) holds potential in accurate determination of relative electron density (RED) and proton stopping power ratio (SPR) but is not widely available.

OBJECTIVE

To demonstrate the feasibility of MV-FBCT using a medical linear accelerator (LINAC) with a 2.5 MV imaging beam, an electronic portal imaging device (EPID) and multileaf collimators (MLCs).

METHODS

MLCs were used to collimate MV beam along z direction to enable a 1 cm width fan-beam. Projection data were acquired within one gantry rotation and preprocessed with in-house developed artifact correction algorithms before the reconstruction. MV-FBCT data were acquired at two dose levels: 30 and 60 monitor units (MUs). A Catphan 604 phantom was used to evaluate basic image quality. A head-sized CIRS phantom with three configurations of tissue-mimicking inserts was scanned and MV-FBCT Hounsfield unit (HU) to RED calibration was established for each insert configuration using linear regression. The determination coefficient ([Formula: see text]) was used to gauge the accuracy of HU-RED calibration. Results were compared with baseline single-energy kilo-voltage treatment planning CT (TP-CT) HU-RED calibration which represented the current standard clinical practice.

RESULTS

The in-house artifact correction algorithms effectively suppressed ring artifact, cupping artifact, and CT number bias in MV-FBCT. Compared to TP-CT, MV-FBCT was able to improve the prediction accuracy of the HU-RED calibration curve for all three configurations of insert materials, with [Formula: see text] > 0.9994 and [Formula: see text] < 0.9990 for MV-FBCT and TP-CT HU-RED calibration curves of soft-tissue inserts, respectively. The measured mean CT numbers of blood-iodine mixture inserts in TP-CT drastically deviated from the fitted values but not in MV-FBCT. Reducing the radiation level from 60 to 30 MU did not decrease the prediction accuracy of the MV-FBCT HU-RED calibration curve.

CONCLUSION

We demonstrated the feasibility of MV-FBCT and its potential in providing more accurate RED estimation.

Stationary computed tomography with source and detector in linear symmetric geometry: Direct filtered backprojection reconstruction

PURPOSE

Inverse-geometry computed tomography (IGCT) could have great potential in medical applications and security inspections, and has been actively investigated in recent years. In this work, we explore a special architecture of IGCT in a stationary configuration: symmetric-geometry computed tomography (SGCT), where the x-ray source and detector are linearly distributed in a symmetric design. A direct filtered backprojection (FBP)-type algorithm is developed to analytically reconstruct images from the SGCT projections.

METHODS

In our proposed SGCT system, a big number of x-ray source points equally distributed along a straight-line trajectory will sequentially fire in an ultra-fast manner in one side, and an equispaced detector whose total length is comparable to that of the source will continuously collect data in the opposite side, as the object to be scanned moves into the imaging plane. We firstly present the overall design of SGCT. An FBP-type reconstruction algorithm is then derived for this unique imaging configuration. With finite length of x-ray source and detector arrays, projection data from one segment of SGCT scan are insufficient for an exact reconstruction. As a result, in practical applications, dual-SGCT scan whose detector segments are placed perpendicular to each other, is of particular interest and is proposed. Two segments of SGCT together can make sure that the passing rays cover at least 180 degrees for each and every point if carefully designed. In general, however, there exists a data redundancy problem for a dual-SGCT. So a weighting strategy is developed to maximize the use of projection data collected while avoid image artifacts. In addition, we further extend the fan-beam SGCT to cone beam and obtain a Feldkamp-Davis-Kress (FDK)-type reconstruction algorithm. Finally, we conduct a set of experimental studies both in simulation and on a prototype SGCT system and validate our proposed methods.

RESULTS

A simulation study using the Shepp-Logan head phantom confirms that CT images can be exactly reconstructed from dual-SGCT scan and that our proposed weighting strategy is able to handle the data redundancy properly. Compared with the rebinning-to-parallel-beam method using the forward projection of an abdominal CT dataset, our proposed method is seen to be less sensitive to data truncation. Our algorithm can achieve 10.64 lp/cm of spatial resolution at 50% modulation transfer functions point, higher than that of the rebinning method which can only reach at 9.42 lp/cm even with extremely fine interpolation. Real experiments of a cylindrical object on a prototype SGCT further prove the effectiveness and practicability of the direct FBP method proposed, with similar level of noise performance to rebinning algorithm.

CONCLUSIONS

A new concept of SGCT with linearly distributed source and detector is investigated in this work, in which spinning of sources and detectors is no longer needed during data acquisition, simplifying its system design, development, and manufacturing. A direct FBP-type algorithm is developed for analytical reconstruction from SGCT projection data. Numerical and real experiments validate our method and show that exact CT image can be reconstructed from dual-SGCT scan, where data redundancy problem can be solved by our proposed weighting function.

Learning to Reconstruct Computed Tomography Images Directly From Sinogram Data Under A Variety of Data Acquisition Conditions

Computed tomography (CT) is widely used in medical diagnosis and non-destructive detection. Image reconstruction in CT aims to accurately recover pixel values from measured line integrals, i.e., the summed pixel values along straight lines. Provided that the acquired data satisfy the data sufficiency condition as well as other conditions regarding the view angle sampling interval and the severity of transverse data truncation, researchers have discovered many solutions to accurately reconstruct the image. However, if these conditions are violated, accurate image reconstruction from line integrals remains an intellectual challenge. In this paper, a deep learning method with a common network architecture, termed iCT-Net, was developed and trained to accurately reconstruct images for previously solved and unsolved CT reconstruction problems with high quantitative accuracy. Particularly, accurate reconstructions were achieved for the case when the sparse view reconstruction problem (i.e., compressed sensing problem) is entangled with the classical interior tomographic problems.

Secured regions of interest (SROIs) in single-pixel imaging

Single-pixel imaging, which is also known as computational ghost imaging, can reconstruct an entire image using one non-spatially resolved detector. However, it often requires a large amount of sampling, severely limiting its application. In this paper, we discuss the implementation of secured regions of interest (SROIs) in single-pixel imaging and illustrate its application using two experiments. Under a limited number of sampling times, we improved the resolution and recovered spectral information of interest in the ROI. Meanwhile, this scheme has high information security with high encryption and has great potential for single-pixel video and compressive multi-spectral single-pixel imaging.

Dual scan CT image recovery from truncated projections

There are computerized tomography (CT) scanners available commercially for imaging small objects and they are often categorized as mini-CT X-ray machines. One major limitation of these machines is their inability to scan large objects with good image quality because of the truncation of projection data. An algorithm is proposed in this work which enables such machines to scan large objects while maintaining the quality of the recovered image.

Image reconstruction in region-of-interest (or interior) digital tomosynthesis (DTS) based on compressed-sensing (CS)

BACKGROUND AND OBJECTIVE

Digital tomosynthesis (DTS) based on filtered-backprojection (FBP) reconstruction requires a full field-of-view (FOV) scan and relatively dense projections, which results in high doses for medical imaging purposes. To overcome these difficulties, we investigated region-of-interest (ROI) or interior DTS reconstruction where the x-ray beam span covers only a small ROI containing a target area.

METHODS

An iterative method based on compressed-sensing (CS) scheme was compared with the FBP-based algorithm for ROI-DTS reconstruction. We implemented both algorithms and performed a systematic simulation and experiments on body and skull phantoms. The image characteristics were evaluated and compared.

RESULTS

The CS-based algorithm yielded much better reconstruction quality in ROI-DTS compared to the FBP-based algorithm, preserving superior image homogeneity, edge sharpening, and in-plane resolution. The image characteristics of the CS-reconstructed images in ROI-DTS were not significantly different from those in full-FOV DTS. The measured CNR value of the CS-reconstructed ROI-DTS image was about 12.3, about 1.9 times larger than that of the FBP-reconstructed ROI-DTS image.

CONCLUSIONS

ROI-DTS images of substantially high accuracy were obtained using the CS-based algorithm and at reduced imaging doses and less computational cost, compared to typical full-FOV DTS images. We expect that the proposed method will be useful for the development of new DTS systems.

A practical local tomography reconstruction algorithm based on a known sub-region

A new method to reconstruct data acquired in a local tomography setup is proposed. This method uses an initial reconstruction and refines it by correcting the low-frequency artifacts, known as the cupping effect. A basis of Gaussian functions is used to correct the initial reconstruction. The coefficients of this basis are found by optimizing iteratively a fidelity term under the constraint of a known sub-region. Using a coarse basis reduces the degrees of freedom of the problem while actually correcting the cupping effect. Simulations show that the known region constraint yields an unbiased reconstruction, in accordance with uniqueness theorems stated in local tomography.

Half-Fan-Based Intensity-Weighted Region-of-Interest Imaging for Low-Dose Cone-Beam CT in Image-Guided Radiation Therapy

Objectives

With the increased use of computed tomography (CT) in clinics, dose reduction is the most important feature people seek when considering new CT techniques or applications. We developed an intensity-weighted region-of-interest (IWROI) imaging method in an exact half-fan geometry to reduce the imaging radiation dose to patients in cone-beam CT (CBCT) for image-guided radiation therapy (IGRT). While dose reduction is highly desirable, preserving the high-quality images of the ROI is also important for target localization in IGRT.

Methods

An intensity-weighting (IW) filter made of copper was mounted in place of a bowtie filter on the X-ray tube unit of an on-board imager (OBI) system such that the filter can substantially reduce radiation exposure to the outer ROI. In addition to mounting the IW filter, the lead-blade collimation of the OBI was adjusted to produce an exact half-fan scanning geometry for a further reduction of the radiation dose. The chord-based rebinned backprojection-filtration (BPF) algorithm in circular CBCT was implemented for image reconstruction, and a humanoid pelvis phantom was used for the IWROI imaging experiment.

Results

The IWROI image of the phantom was successfully reconstructed after beam-quality correction, and it was registered to the reference image within an acceptable level of tolerance. Dosimetric measurements revealed that the dose is reduced by approximately 61% in the inner ROI and by 73% in the outer ROI compared to the conventional bowtie filter-based half-fan scan.

Conclusions

The IWROI method substantially reduces the imaging radiation dose and provides reconstructed images with an acceptable level of quality for patient setup and target localization. The proposed half-fan-based IWROI imaging technique can add a valuable option to CBCT in IGRT applications.

A two-step filtering-based iterative image reconstruction method for interior tomography

The optimization-based method that utilizes the additional sparse prior of region-of-interest (ROI) image, such as total variation, has been the subject of considerable research in problems of interior tomography reconstruction. One challenge for optimization-based iterative ROI image reconstruction is to build the relationship between ROI image and truncated projection data. When the reconstruction support region is smaller than the original object, an unsuitable representation of data fidelity may lead to bright truncation artifacts in the boundary region of field of view. In this work, we aim to develop an iterative reconstruction method to suppress the truncation artifacts and improve the image quality for direct ROI image reconstruction. A novel reconstruction approach is proposed based on an optimization problem involving a two-step filtering-based data fidelity. Data filtering is achieved in two steps: the first takes the derivative of projection data; in the second step, Hilbert filtering is applied in the differentiated data. Numerical simulations and real data reconstructions have been conducted to validate the new reconstruction method. Both qualitative and quantitative results indicate that, as theoretically expected, the proposed method brings reasonable performance in suppressing truncation artifacts and preserving detailed features. The presented local reconstruction method based on the two-step filtering strategy provides a simple and efficient approach for the iterative reconstruction from truncated projections.

Synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON): A statistical model based iterative image reconstruction method to eliminate limited-view artifacts and to mitigate the temporal-average artifacts in time-resolved CT

PURPOSE

In x-ray computed tomography (CT), a violation of the Tuy data sufficiency condition leads to limited-view artifacts. In some applications, it is desirable to use data corresponding to a narrow temporal window to reconstruct images with reduced temporal-average artifacts. However, the need to reduce temporal-average artifacts in practice may result in a violation of the Tuy condition and thus undesirable limited-view artifacts. In this paper, the authors present a new iterative reconstruction method, synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON), to eliminate limited-view artifacts using data acquired within an ultranarrow temporal window that severely violates the Tuy condition.

METHODS

In time-resolved contrast enhanced CT acquisitions, image contrast dynamically changes during data acquisition. Each image reconstructed from data acquired in a given temporal window represents one time frame and can be denoted as an image vector. Conventionally, each individual time frame is reconstructed independently. In this paper, all image frames are grouped into a spatial-temporal image matrix and are reconstructed together. Rather than the spatial and/or temporal smoothing regularizers commonly used in iterative image reconstruction, the nuclear norm of the spatial-temporal image matrix is used in SMART-RECON to regularize the reconstruction of all image time frames. This regularizer exploits the low-dimensional structure of the spatial-temporal image matrix to mitigate limited-view artifacts when an ultranarrow temporal window is desired in some applications to reduce temporal-average artifacts. Both numerical simulations in two dimensional image slices with known ground truth and in vivo human subject data acquired in a contrast enhanced cone beam CT exam have been used to validate the proposed SMART-RECON algorithm and to demonstrate the initial performance of the algorithm. Reconstruction errors and temporal fidelity of the reconstructed images were quantified using the relative root mean square error (rRMSE) and the universal quality index (UQI) in numerical simulations. The performance of the SMART-RECON algorithm was compared with that of the prior image constrained compressed sensing (PICCS) reconstruction quantitatively in simulations and qualitatively in human subject exam.

RESULTS

In numerical simulations, the 240(∘) short scan angular span was divided into four consecutive 60(∘) angular subsectors. SMART-RECON enables four high temporal fidelity images without limited-view artifacts. The average rRMSE is 16% and UQIs are 0.96 and 0.95 for the two local regions of interest, respectively. In contrast, the corresponding average rRMSE and UQIs are 25%, 0.78, and 0.81, respectively, for the PICCS reconstruction. Note that only one filtered backprojection image can be reconstructed from the same data set with an average rRMSE and UQIs are 45%, 0.71, and 0.79, respectively, to benchmark reconstruction accuracies. For in vivo contrast enhanced cone beam CT data acquired from a short scan angular span of 200(∘), three 66(∘) angular subsectors were used in SMART-RECON. The results demonstrated clear contrast difference in three SMART-RECON reconstructed image volumes without limited-view artifacts. In contrast, for the same angular sectors, PICCS cannot reconstruct images without limited-view artifacts and with clear contrast difference in three reconstructed image volumes.

CONCLUSIONS

In time-resolved CT, the proposed SMART-RECON method provides a new method to eliminate limited-view artifacts using data acquired in an ultranarrow temporal window, which corresponds to approximately 60(∘) angular subsectors.

Dynamic intensity-weighted region of interest imaging for conebeam CT

BACKGROUND

Patient dose from image guidance in radiotherapy is small compared to the treatment dose. However, the imaging beam is untargeted and deposits dose equally in tumor and healthy tissues. It is desirable to minimize imaging dose while maintaining efficacy.

OBJECTIVE

Image guidance typically does not require full image quality throughout the patient. Dynamic filtration of the kV beam allows local control of CT image noise for high quality around the target volume and lower quality elsewhere, with substantial dose sparing and reduced scatter fluence on the detector.

METHODS

The dynamic Intensity-Weighted Region of Interest (dIWROI) technique spatially varies beam intensity during acquisition with copper filter collimation. Fluence is reduced by 95% under the filters with the aperture conformed dynamically to the ROI during cone-beam CT scanning. Preprocessing to account for physical effects of the collimator before reconstruction is described.

RESULTS

Reconstructions show image quality comparable to a standard scan in the ROI, with higher noise and streak artifacts in the outer region but still adequate quality for patient localization. Monte Carlo modeling shows dose reduction by 10-15% in the ROI due to reduced scatter, and up to 75% outside.

CONCLUSIONS

The presented technique offers a method to reduce imaging dose by accepting increased image noise outside the ROI, while maintaining full image quality inside the ROI.

Dynamic detector offsets for field of view extension in C-arm computed tomography with application to weight-bearing imaging

PURPOSE

In C-arm computed tomography (CT), the field of view (FOV) is often not sufficient to acquire certain anatomical structures, e.g., a full hip or thorax. Proposed methods to extend the FOV use a fixed detector displacement and a 360° scan range to double the radius of the FOV. These trajectories are designed for circular FOVs. However, there are cases in which the required FOV is not circular but rather an ellipsoid.

METHODS

In this work, the authors show that in fan-beam CT, the use of a dynamically adjusting detector offset can reduce the required scan range when using a noncircular FOV. Furthermore, the authors present an analytic solution to determine the minimal required scan ranges for elliptic FOVs given a certain detector size and an algorithmic approach for arbitrary FOVs.

RESULTS

The authors show that the proposed method can result in a substantial reduction of the required scan range. Initial reconstructions of data sets acquired with our new minimal trajectory yielded image quality comparable to reconstructions of data acquired using a fixed detector offset and a full 360° rotation.

CONCLUSIONS

Our results show a promising reduction of the necessary scan range especially for ellipsoidal objects that extend the FOV. In noncircular FOVs, there exists a set of solutions that allow a trade-off between detector size and scan range.

Data consistency conditions for truncated fanbeam and parallel projections

PURPOSE

In image reconstruction from projections, data consistency conditions (DCCs) are mathematical relationships that express the overlap of information between ideal projections. DCCs have been incorporated in image reconstruction procedures for positron emission tomography, single photon emission computed tomography, and x-ray computed tomography (CT). Building on published fanbeam DCCs for nontruncated projections along a line, the authors recently announced new DCCs that can be applied to truncated parallel projections in classical (two-dimensional) image reconstruction. These DCCs take the form of polynomial expressions for a weighted backprojection of the projections. The purpose of this work was to present the new DCCs for truncated parallel projections, to extend these conditions to truncated fanbeam projections on a circular trajectory, to verify the conditions with numerical examples, and to present a model of how DCCs could be applied with a toy problem in patient motion estimation with truncated projections.

METHODS

A mathematical derivation of the new parallel DCCs was performed by substituting the underlying imaging equation into the mathematical expression for the weighted backprojection and demonstrating the resulting polynomial form. This DCC result was extended to fanbeam projections by a substitution of parallel to fanbeam variables. Ideal fanbeam projections of a simple mathematical phantom were simulated and the DCCs for these projections were evaluated by fitting polynomials to the weighted backprojection. For the motion estimation problem, a parametrized motion was simulated using a dynamic version of the mathematical phantom, and both noiseless and noisy fanbeam projections were simulated for a full circular trajectory. The fanbeam DCCs were applied to extract the motion parameters, which allowed the motion contamination to be removed from the projections. A reconstruction was performed from the corrected projections.

RESULTS

The mathematical derivation revealed the anticipated polynomial behavior. The conversion to fanbeam variables led to a straight-forward weighted fanbeam backprojection which yielded the same function and therefore the same polynomial behavior as occurred in the parallel case. Plots of the numerically calculated DCCs showed polynomial behavior visually indistinguishable from the fitted polynomials. For the motion estimation problem, the motion parameters were satisfactorily recovered and ten times more accurately for the noise-free case. The reconstructed images showed that only a faint trace of the motion blur was still visible after correction from the noisy motion-contaminated projections.

CONCLUSIONS

New DCCs have been established for fanbeam and parallel projections, and these conditions have been validated using numerical experiments with truncated projections. It has been shown how these DCCs could be applied to extract parameters of unwanted physical effects in tomographic imaging, even with truncated projections.

Reconstructing cone-beam CT with spatially varying qualities for adaptive radiotherapy: a proof-of-principle study

With the aim of maximally reducing imaging dose while meeting requirements for adaptive radiation therapy (ART), we propose in this paper a new cone beam CT (CBCT) acquisition and reconstruction method that delivers images with a low noise level inside a region of interest (ROI) and a relatively high noise level outside the ROI. The acquired projection images include two groups: densely sampled projections at a low exposure with a large field of view (FOV) and sparsely sampled projections at a high exposure with a small FOV corresponding to the ROI. A new algorithm combining the conventional filtered back-projection algorithm and the tight-frame iterative reconstruction algorithm is also designed to reconstruct the CBCT based on these projection data. We have validated our method on a simulated head-and-neck (HN) patient case, a semi-real experiment conducted on a HN cancer patient under a full-fan scan mode, as well as a Catphan phantom under a half-fan scan mode. Relative root-mean-square errors (RRMSEs) of less than 3% for the entire image and ~1% within the ROI compared to the ground truth have been observed. These numbers demonstrate the ability of our proposed method to reconstruct high-quality images inside the ROI. As for the part outside ROI, although the images are relatively noisy, it can still provide sufficient information for radiation dose calculations in ART. Dose distributions calculated on our CBCT image and on a standard CBCT image are in agreement, with a mean relative difference of 0.082% inside the ROI and 0.038% outside the ROI. Compared with the standard clinical CBCT scheme, an imaging dose reduction of approximately 3-6 times inside the ROI was achieved, as well as an 8 times outside the ROI. Regarding computational efficiency, it takes 1-3 min to reconstruct a CBCT image depending on the number of projections used. These results indicate that the proposed method has the potential for application in ART.

Improving image accuracy of region-of-interest in cone-beam CT using prior image

In diagnostic follow-ups of diseases, such as calcium scoring in kidney or fat content assessment in liver using repeated CT scans, quantitatively accurate and consistent CT values are desirable at a low cost of radiation dose to the patient. Region of-interest (ROI) imaging technique is considered a reasonable dose reduction method in CT scans for its shielding geometry outside the ROI. However, image artifacts in the reconstructed images caused by missing data outside the ROI may degrade overall image quality and, more importantly, can decrease image accuracy of the ROI substantially. In this study, we propose a method to increase image accuracy of the ROI and to reduce imaging radiation dose via utilizing the outside ROI data from prior scans in the repeated CT applications. We performed both numerical and experimental studies to validate our proposed method. In a numerical study, we used an XCAT phantom with its liver and stomach changing their sizes from one scan to another. Image accuracy of the liver has been improved as the error decreased from 44.4 HU to -0.1 HU by the proposed method, compared to an existing method of data extrapolation to compensate for the missing data outside the ROI. Repeated cone-beam CT (CBCT) images of a patient who went through daily CBCT scans for radiation therapy were also used to demonstrate the performance of the proposed method experimentally. The results showed improved image accuracy inside the ROI. The magnitude of error decreased from -73.2 HU to 18 HU, and effectively reduced image artifacts throughout the entire image.

Low-dose and scatter-free cone-beam CT imaging using a stationary beam blocker in a single scan: phantom studies

Excessive imaging dose from repeated scans and poor image quality mainly due to scatter contamination are the two bottlenecks of cone-beam CT (CBCT) imaging. Compressed sensing (CS) reconstruction algorithms show promises in recovering faithful signals from low-dose projection data but do not serve well the needs of accurate CBCT imaging if effective scatter correction is not in place. Scatter can be accurately measured and removed using measurement-based methods. However, these approaches are considered unpractical in the conventional FDK reconstruction, due to the inevitable primary loss for scatter measurement. We combine measurement-based scatter correction and CS-based iterative reconstruction to generate scatter-free images from low-dose projections. We distribute blocked areas on the detector where primary signals are considered redundant in a full scan. Scatter distribution is estimated by interpolating/extrapolating measured scatter samples inside blocked areas. CS-based iterative reconstruction is finally carried out on the undersampled data to obtain scatter-free and low-dose CBCT images. With only 25% of conventional full-scan dose, our method reduces the average CT number error from 250 HU to 24 HU and increases the contrast by a factor of 2.1 on Catphan 600 phantom. On an anthropomorphic head phantom, the average CT number error is reduced from 224 HU to 10 HU in the central uniform area.

Gel'fand-Graev's reconstruction formula in the 3D real space

PURPOSE

Gel'fand and Graev performed classical work on the inversion of integral transforms in different spaces [Gel'fand and Graev, Funct. Anal. Appl. 25(1) 1-5 (1991)]. This paper discusses their key results for further research and development.

METHODS

The Gel'fand-Graev inversion formula reveals a fundamental relationship between projection data and the Hilbert transform of an image to be reconstructed. This differential backprojection (DBP)∕backprojection filtration (BPF) approach was rediscovered in the CT field, and applied in important applications such as reconstruction from truncated projections, interior tomography, and limited-angle tomography. Here the authors present the Gel'fand-Graev inversion formula in a 3D setting assuming the 1D x-ray transform.

RESULTS

The pseudodifferential operator is a powerful theoretical tool. There is a fundamental mathematical link between the Gel'fand-Graev formula and the DBP (or BPF) approach in the case of the 1D x-ray transform in a 3D real space.

CONCLUSIONS

This paper shows the power of mathematics for tomographic imaging and the value of a pure theoretical finding, which may appear quite irrelevant to daily healthcare at the first glance.

Volume-of-change cone-beam CT for image-guided surgery

C-arm cone-beam CT (CBCT) can provide intraoperative 3D imaging capability for surgical guidance, but workflow and radiation dose are the significant barriers to broad utilization. One main reason is that each 3D image acquisition requires a complete scan with a full radiation dose to present a completely new 3D image every time. In this paper, we propose to utilize patient-specific CT or CBCT as prior knowledge to accurately reconstruct the aspects of the region that have changed by the surgical procedure from only a sparse set of x-rays. The proposed methods consist of a 3D-2D registration between the prior volume and a sparse set of intraoperative x-rays, creating digitally reconstructed radiographs (DRRs) from the registered prior volume, computing difference images by subtracting DRRs from the intraoperative x-rays, a penalized likelihood reconstruction of the volume of change (VOC) from the difference images, and finally a fusion of VOC reconstruction with the prior volume to visualize the entire surgical field. When the surgical changes are local and relatively small, the VOC reconstruction involves only a small volume size and a small number of projections, allowing less computation and lower radiation dose than is needed to reconstruct the entire surgical field. We applied this approach to sacroplasty phantom data obtained from a CBCT test bench and vertebroplasty data with a fresh cadaver acquired from a C-arm CBCT system with a flat-panel detector. The VOCs were reconstructed from a varying number of images (10-66 images) and compared to the CBCT ground truth using four different metrics (mean squared error, correlation coefficient, structural similarity index and perceptual difference model). The results show promising reconstruction quality with structural similarity to the ground truth close to 1 even when only 15-20 images were used, allowing dose reduction by the factor of 10-20.

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom

Mathematical phantoms are essential for the development and early stage evaluation of image reconstruction algorithms in x-ray computed tomography (CT). This note offers tools for computer simulations using a two-dimensional (2D) phantom that models the central axial slice through the FORBILD head phantom. Introduced in 1999, in response to a need for a more robust test, the FORBILD head phantom is now seen by many as the gold standard. However, the simple Shepp-Logan phantom is still heavily used by researchers working on 2D image reconstruction. Universal acceptance of the FORBILD head phantom may have been prevented by its significantly higher complexity: software that allows computer simulations with the Shepp-Logan phantom is not readily applicable to the FORBILD head phantom. The tools offered here address this problem. They are designed for use with Matlab®, as well as open-source variants, such as FreeMat and Octave, which are all widely used in both academia and industry. To get started, the interested user can simply copy and paste the codes from this PDF document into Matlab® M-files.

A feasibility study on gamma-ray tomography by Monte Carlo simulation for development of portable tomographic system

The electron beam X-ray tomographic scanner has been used in industrial and medical field since it was developed two decades ago. However, X-ray electron beam tomography has remained as indoor equipment because of its bulky hardware of X-ray generation devices. By replacing X-ray devices of electron beam CT with a gamma-ray source, a tomographic system can be a portable device. This paper introduces analysis and simulation results on industrial gamma-ray tomographic system with scanning geometry similar to electron beam CT. The gamma-ray tomographic system is introduced through the geometrical layout and analysis on non-uniformly distributed problem. The proposed system adopts clamp-on type device to actualize portable industrial system. MCNPx is used to generate virtual experimental data. Pulse height spectra from F8 tally of MCNPx are obtained for single channel counting data of photo-peak and gross counting. Photo-peak and gross counting data are reconstructed for the cross-sectional image of simulation phantoms by ART, Total Variation algorithm and ML-EM. Image reconstruction results from Monte Carlo simulation show that the proposed tomographic system can provide the image solution for industrial objects. Those results provide the preliminary data for the tomographic scanner, which will be developed in future work.

Multiresolution reconstruction for cone-beam tomography from raw data projections using 3D ridgelets

This paper presents a novel method which reconstructs any desired 3D image resolution from raw cone-beam CT data. X-ray attenuation through the object is approximated using ridgelet basis functions which allow us to have multiresolution representation levels. Since the Radon data have preferential orientations by nature, a spherical wavelet transform is used to compute the ridgelet coefficients from the Radon shell data. The whole method uses the classical Grangeat's relation for computing derivatives of the Radon data which are then integrated and projected to a spherical wavelet representation and back-reconstructed using a modified version of the well known back-projection algorithm. Unlike previous reconstruction methods, this proposal uses a multiscale representation of the Radon data and therefore allows fast display of low-resolution data level.

Hybrid cone-beam tomographic reconstruction: incorporation of prior anatomical models to compensate for missing data

We propose a method for improving the quality of cone-beam tomographic reconstruction done with a C-arm. C-arm scans frequently suffer from incomplete information due to image truncation, limited scan length, or other limitations. Our proposed "hybrid reconstruction" method injects information from a prior anatomical model, derived from a subject-specific computed tomography (CT) or from a statistical database (atlas), where the C-arm X-ray data is missing. This significantly reduces reconstruction artifacts with little loss of true information from the X-ray projections. The methods consist of constructing anatomical models, fast rendering of digitally reconstructed radiograph (DRR) projections of the models, rigid or deformable registration of the model and the X-ray images, and fusion of the DRR and X-ray projections, all prior to a conventional filtered back-projection algorithm. Our experiments, conducted with a mobile image intensifier C-arm, demonstrate visually and quantitatively the contribution of data fusion to image quality, which we assess through comparison to a "ground truth" CT. Importantly, we show that a significantly improved reconstruction can be obtained from a C-arm scan as short as 90° by complementing the observed projections with DRRs of two prior models, namely an atlas and a preoperative same-patient CT. The hybrid reconstruction principles are applicable to other types of C-arms as well.

Balancing dose and image registration accuracy for cone beam tomosynthesis (CBTS) for breast patient setup

PURPOSE

To balance dose reduction and image registration accuracy in breast setup imaging. In particular, the authors demonstrate the relationship between scan angle and dose delivery for cone beam tomosynthesis (CBTS) when employed for setup verification of breast cancer patients with surgical clips.

METHODS

The dose measurements were performed in a female torso phantom for varying scan angles of CBTS. Setup accuracy was measured using three registration methods: Clip centroid localization accuracy and the accuracy of two semiautomatic registration algorithms. The dose to the organs outside of the ipsilateral breast and registration accuracy information were compared to determine the optimal scan angle for CBTS for breast patient setup verification. Isocenter positions at the center of the patient and at the breast-chest wall interface were considered.

RESULTS

Image registration accuracy was within 1 mm for the CBTS scan angles theta above 20 degrees for some scenarios and as large as 80 degrees for the worst case, depending on the imaged breast and registration algorithm. Registration accuracy was highest based on clip centroid localization. For left and right breast imaging with the isocenter at the chest wall, the dose to the contralateral side of the patient was very low (<0.5 cGy) for all scan angles considered. For central isocenter location, the optimal scan angles were 30 degrees - 50 degrees for the left breast imaging and 40 degrees - 50 degrees for the right breast imaging, with the difference due to the geometric asymmetry of the current clinical imaging system.

CONCLUSIONS

The optimal scan angles for CBTS imaging were found to be between 10 degrees and 50 degrees, depending on the isocenter location and ipsilateral breast. Use of the isocenter at the breast-chest wall locations always resulted in greater accuracy of image registration (<1 mm) at smaller angles (10 degrees - 20 degrees) and at lower doses (<0.1 cGy) to the contralateral organs. For chest wall isocenters, doses delivered to organs outside of the target breast were much smaller than the scattered and leakage doses of the treatment beams. The complete volumetric information of all clips in the region of interest, combined with the small dose to the contralateral organs and the small scan angle, could result in an advantage for small angle CBTS with off center isocenters over simple orthogonal pairs.

Dual resolution cone beam breast CT: a feasibility study

PURPOSE

In this study, the authors investigated the feasibility of a dual resolution volume-of-interest (VOI) cone beam breast CT technique and compared two implementation approaches in terms of dose saving and scatter reduction.

METHODS

With this technique, a lead VOI mask with an opening is inserted between the x-ray source and the breast to deliver x-ray exposure to the VOI while blocking x rays outside the VOI. A CCD detector is used to collect the high resolution projection data of the VOI. Low resolution cone beam CT (CBCT) images of the entire breast, acquired with a flat panel (FP) detector, were used to calculate the projection data outside the VOI with the ray-tracing reprojection method. The Feldkamp-Davis-Kress filtered backprojection algorithm was used to reconstruct the dual resolution 3D images. Breast phantoms with 180 microm and smaller microcalcifications (MCs) were imaged with both FP and FP-CCD dual resolution CBCT systems, respectively. Two approaches of implementing the dual resolution technique, breast-centered approach and VOI-centered approach, were investigated and evaluated for dose saving and scatter reduction with Monte Carlo simulation using a GEANT4 package.

RESULTS

The results showed that the breast-centered approach saved more breast absorbed dose than did VOI-centered approach with similar scatter reduction. The MCs in fatty breast phantom, which were invisible with FP CBCT scan, became visible with the FP-CCD dual resolution CBCT scan.

CONCLUSIONS

These results indicate potential improvement of the image quality inside the VOI with reduced breast dose both inside and outside the VOI.

Radiation dose reduction in computed tomography: techniques and future perspective

Despite universal consensus that computed tomography (CT) overwhelmingly benefits patients when used for appropriate indications, concerns have been raised regarding the potential risk of cancer induction from CT due to the exponentially increased use of CT in medicine. Keeping radiation dose as low as reasonably achievable, consistent with the diagnostic task, remains the most important strategy for decreasing this potential risk. This article summarizes the general technical strategies that are commonly used for radiation dose management in CT. Dose-management strategies for pediatric CT, cardiac CT, dual-energy CT, CT perfusion and interventional CT are specifically discussed, and future perspectives on CT dose reduction are presented.

Validation of attenuation correction using transmission truncation compensation with a small field of view dedicated cardiac SPECT camera system

BACKGROUND

Although attenuation correction (AC) has been successfully applied to large field of view (LFOV) cameras, applicability to small field of view (SFOV) cameras is a concern due to truncation. This study compared perfusion images between a LFOV and SFOV camera with truncation compensation, using the same AC solution.

METHODS AND RESULTS

Seventy-eight clinically referred patients underwent rest-stress single-photon emission computed tomography (SPECT) using both a SFOV and LFOV camera in a randomized sequence. Blinded images were interpreted by a consensus of three experienced readers. The percentage of normal images for SFOV and LFOV was significantly higher with than without AC (72% vs 44% and 72% vs 49%, both P < .001). Interpretive agreement between cameras was better with than without AC (kappa = 0.736 to 0.847 vs 0.545 to 0.774). Correlation for the summed stress score was higher with than without AC (r (2) = 0.892 vs 0.851, both P < 0.001) while Bland Altman analysis demonstrated narrower limits with than without AC (4.0 to -4.3 vs 5.9 to -5.6).

CONCLUSION

Attenuation correction using truncation compensation with a SFOV camera yields similar results to a LFOV camera. The higher interpretive agreement between cameras after attenuation correction suggests that such images are preferable to non-attenuation-corrected images.

SOLVING THE INTERIOR PROBLEM OF COMPUTED TOMOGRAPHY USING A PRIORI KNOWLEDGE

The case of incomplete tomographic data for a compactly supported attenuation function is studied. When the attenuation function is a priori known in a subregion, we show that a reduced set of measurements is enough to uniquely determine the attenuation function over all the space. Furthermore, we found stability estimates showing that reconstruction can be stable near the region where the attenuation is known. These estimates also suggest that reconstruction stability collapses quickly when approaching the set of points that are viewed under less than 180 degrees. This paper may be seen as a continuation of the work "Truncated Hilbert transform and Image reconstruction from limited tomographic data" that was published in Inverse Problems in 2006. This continuation tackles new cases of incomplete data that could be of interest in applications of computed tomography.

Region-of-interest image reconstruction in circular cone-beam microCT

Cone-beam microcomputed tomography (microCT) is one of the most popular choices for small animal imaging which is becoming an important tool for studying animal models with transplanted diseases. Region-of-interest (ROI) imaging techniques in CT, which can reconstruct an ROI image from the projection data set of the ROI, can be used not only for reducing imaging-radiation exposure to the subject and scatters to the detector but also for potentially increasing spatial resolution of the reconstructed images. Increasing spatial resolution in microCT images can facilitate improved accuracy in many assessment tasks. A method proposed previously for increasing CT image spatial resolution entails the exploitation of the geometric magnification in cone-beam CT. Due to finite detector size, however, this method can lead to data truncation for a large geometric magnification. The Feldkamp-Davis-Kress (FDK) algorithm yields images with artifacts when truncated data are used, whereas the recently developed backprojection filtration (BPF) algorithm is capable of reconstructing ROI images without truncation artifacts from truncated cone-beam data. We apply the BPF algorithm to reconstructing ROI images from truncated data of three different objects acquired by our circular cone-beam microCT system. Reconstructed images by use of the FDK and BPF algorithms from both truncated and nontruncated cone-beam data are compared. The results of the experimental studies demonstrate that, from certain truncated data, the BPF algorithm can reconstruct ROI images with quality comparable to that reconstructed from nontruncated data. In contrast, the FDK algorithm yields ROI images with truncation artifacts. Therefore, an implication of the studies is that, when truncated data are acquired with a configuration of a large geometric magnification, the BPF algorithm can be used for effective enhancement of the spatial resolution of a ROI image.

Tiny a priori knowledge solves the interior problem in computed tomography

Based on the concept of differentiated backprojection (DBP) (Noo et al 2004 Phys. Med. Biol. 49 3903, Pan et al 2005 Med. Phys. 32 673, Defrise et al 2006 Inverse Problems 22 1037), this paper shows that the solution to the interior problem in computed tomography is unique if a tiny a priori knowledge on the object f(x, y) is available in the form that f(x, y) is known on a small region located inside the region of interest. Furthermore, we advance the uniqueness result to obtain more general uniqueness results which can be applied to a wider class of imaging configurations. We also develop a reconstruction algorithm which can be considered an extension of the DBP-POCS (projection onto convex sets) method described by Defrise et al (2006 Inverse Problems 22 1037), where we not only extend this method to the interior problem but also introduce a new POCS algorithm to reduce computational cost. Finally, we present experimental results which show evidence that the inversion corresponding to each obtained uniqueness result is stable.

Even more inversion formulas for the 2D Radon Transform of functions of compact and convex support

In 2004, Clackdoyle and Noo published a class of inversion formulas for the 2D Radon Transform which depends on the known radius of support of the unknown function. In this work, we extend this class of inversion formulas from functions of circular support to functions with any compact and convex support. We point out the potential benefits of these new inversion formulas in the context of reconstruction from truncated projections. A preliminary implementation of these new inversion formulas is also presented.

Extension of the reconstruction field of view and truncation correction using sinogram decomposition

We propose a novel truncation correction algorithm that completes unmeasured data outside of the scan field of view, which allows extending the reconstruction field of view. When a patient extends outside the detector coverage the projection data are transversely truncated, which causes severe artifacts. The proposed method utilizes the idea of sinogram decomposition, where we consider sinogram curves corresponding to image points outside the field of view. We propose two ways to estimate the truncated data, one based on the minimum value along the sinogram curve, and the other based on the data values near the edge of truncation. Both estimation methods are combined to achieve uniform image quality improvement from the edge of truncation to the outer side of the extended region. In our evaluation with simulated and real projection data we compare the proposed method with existing methods and investigate the dependence on the amount of truncation. The evaluation shows that the proposed method handles cases when truncation is present on both sides of the detector, or when a high-contrast object is located outside the field of view.

Local cone-beam tomography image reconstruction on chords

We develop reconstruction algorithms for local cone-beam tomography for use with generalized scanning trajectories. The algorithms are grounded theoretically in a recently developed chord-based theory for exact image reconstruction and principles of lambda tomography. Being chord based, they are distinct mathematically and conceptually from conventional local tomography reconstruction algorithms. The salient feature of our algorithms is that they permit reconstruction of discontinuities in the profiles of the object function along chords. By consideration of all possible chords, a 3D image that describes the locations of object discontinuities can be reconstructed. Results from microlocal analysis are applied for understanding the object features that can be reconstructed stably by use of the algorithms. A computer-simulation study is conducted to demonstrate the algorithms and compare their performance with an existing algorithm.

Shear-based fast hierarchical backprojection for parallel-beam tomography

We introduce a family of fast algorithms for 2-D parallel-beam tomographic backprojection. They aggregate the projections in a hierarchical structure involving the shearing and addition of sparsely sampled images. The algorithms achieve a computational cost of O(N(2) log P), when backprojecting an N x N pixel image from P projections. The algorithms provide a systematic means, guided by a Fourier-domain interpretation, to adjust and optimize the tradeoff between computational cost and accuracy. In an example with N = 512 and P = 1458 the algorithms provide high accuracy, with more than an order of magnitude reduction in operation counts.

A cone-beam tomography system with a reduced size planar detector: a backprojection-filtration reconstruction algorithm as well as numerical and practical experiments

In a traditional cone-beam computed tomography (CT) system, the cost of product and computation is very high. In this paper, we develop a transversely truncated cone-beam X-ray CT system with a reduced-size detector positioned off-center, in which X-ray beams only cover half of the object. The existing filtered backprojection (FBP) or backprojection-filtration (BPF) algorithms are not directly applicable in this new system. Hence, we develop a BPF-type direct backprojection algorithm. Different from the traditional rebinning methods, our algorithm directly backprojects the pretreated projection data without rebinning. This makes the algorithm compact and computationally more efficient. Because of avoiding interpolation errors of rebinning process, higher spatial resolution is obtained. Finally, some numerical simulations and practical experiments are done to validate the proposed algorithm and compare with rebinning algorithm.

Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning

The long object problem is practically important and theoretically challenging. To solve the long object problem, spiral cone-beam CT was first proposed in 1991, and has been extensively studied since then. As a main feature of the next generation medical CT, spiral cone-beam CT has been greatly improved over the past several years, especially in terms of exact image reconstruction methods. Now, it is well established that volumetric images can be exactly and efficiently reconstructed from longitudinally truncated data collected along a rather general scanning trajectory. Here we present an overview of some key results in this area.

Two-dimensional iterative region-of-interest (ROI) reconstruction from truncated projection data

A small detector or limited gantry rotation angles may cause data truncation, in which case the entire object cannot be completely reconstructed. However, a small region of interest (ROI) may be recoverable in certain truncation situations. Two analytical methods have been proposed for exact ROI reconstruction. Here we evaluate the capability of ROI reconstruction using an maximum-likelihood expectation-maximization (ML-EM) method, which directly solves the inverse problem of the system equations. ROI reconstruction using the ML-EM method is compared with that using the two analytical methods. Comparisons are based on reconstructions of four specifically designed, computer-simulated truncation cases. In the simulation, each reconstructed ROI is coupled with its counterpart in the nontruncated case to evaluate the accuracy of the reconstructed ROI. We found that, (a) in two truncation situations the ROI can be reconstructed by both the analytical methods and the two-dimensional ML-EM method, but the ML-EM method may produce a larger ROI; (b) for a truncation case [Fig. 3(c)] that neither analytical algorithm is applicable, the ML-EM method provides a quantitative ROI reconstruction; and (c) for the well-known "interior" truncation problem, neither the analytical methods nor the ML-EM method can perform an exact ROI reconstruction, but the ML-EM method provides informative ROI images. We also propose an analysis using the truncated projection matrix and its Moore-Penrose inverse matrix which can help to determine the recoverable ROI using iterative methods for a given truncation situation.

Intraoperative cone-beam CT for guidance of head and neck surgery: Assessment of dose and image quality using a C-arm prototype

Cone-beam computed tomography (CBCT) with a flat-panel detector represents a promising modality for intraoperative imaging in interventional procedures, demonstrating sub-mm three-dimensional (3D) spatial resolution and soft-tissue visibility. Measurements of patient dose and in-room exposure for CBCT-guided head and neck surgery are reported, and the 3D imaging performance as a function of dose and other acquisition/reconstruction parameters is investigated. Measurements were performed on a mobile isocentric C-arm (Siemens PowerMobil) modified in collaboration with Siemens Medical Solutions (Erlangen, Germany) to provide flat-panel CBCT. Imaging dose was measured in a custom-built 16 cm cylindrical head phantom at four positions (isocenter, anterior, posterior, and lateral) as a function of kVp (80-120 kVp) and C-arm trajectory ("tube-under" and "tube-over" half-rotation orbits). At 100 kVp, for example ("tube-under" orbit), the imaging dose was 0.059 (isocenter), 0.022 (anterior), 0.10 (posterior), and 0.056 (lateral) mGy/ mAs, with scans at approximately 50 and approximately 170 mAs typical for visualization of bony and soft-tissue structures, respectively. Dose to radiosensitive structures (viz., the eyes and thyroid) were considered in particular: significant dose sparing to the eyes (a factor of 5) was achieved using a "tube-under" (rather than "tube-over") half-rotation orbit; a thyroid shield (0.5 mm Pb-equivalent) gave moderate reduction in thyroid dose due to x-ray scatter outside the primary field of view. In-room exposure was measured at positions around the operating table and up to 2 m from isocenter. A typical CBCT scan (10 mGy to isocenter) gave in-air exposure ranging from 29 mR (0.26 mSv) at 35 cm from isocenter, to <0.5 mR (<0.005 mSv) at 2 m from isocenter. Three-dimensional (3D) image quality was assessed in CBCT reconstructions of an anthropomorphic head phantom containing contrast-detail spheres (11-103 HU; 1.6-12.7 mm) and a natural human skeleton. The contrast-to-noise ratio (CNR) was evaluated across a broad range of dose (0.6-23.3 mGy). CNR increased as the square root of dose, with excellent visualization of bony and soft-tissue structures achieved at approximately 3 mGy (0.10 mSv) and approximately 10 mGy (0.35 mSv), respectively. The prototype C-arm demonstrates CBCT image quality sufficient for guidance of head and neck procedures based on soft-tissue and bony anatomy at dose levels low enough for repeat intraoperative imaging, with total dose over the course of the procedure comparable to or less than the effective dose of a typical (2 mSv) diagnostic CT of the head.

Chord-based image reconstruction in cone-beam CT with a curved detector

Modern computed tomography (CT) scanners use cone-beam configurations for increasing volume coverage, improving x-ray-tube utilization, and yielding isotropic spatial resolution. Recently, there have been significant developments in theory and algorithms for exact image reconstruction from cone-beam projections. In particular, algorithms have been proposed for image reconstruction on chords; and advantages over the existing algorithms offered by the chord-based algorithms include the high flexibility of exact image reconstruction for general scanning trajectories and the capability of exact reconstruction of images within a region of interest from truncated data. These chord-based algorithms have been developed only for flat-panel detectors. Many cone-beam CT scanners employ curved detectors for important practical considerations. Therefore, in this work, we have derived chord-based algorithms for a curved detector so that they can be applied to reconstructing images directly from data acquired by use of a CT scanner with a curved detector. We have also conducted preliminary numerical studies to demonstrate and evaluate the reconstruction properties of the derived chord-based algorithms for curved detectors.

Image reconstruction for transmission tomography when projection data are incomplete

Two iterative methods are developed for forming a maximum-likelihood estimate of the attenuation density in a patient or object for transmission tomography when projection data are incomplete. The methods converge monotonically to the same limit points. Results of testing the methods with both simulated and real data are given.

Region of interest reconstruction from truncated data in circular cone-beam CT

The circular scanning trajectory is one of the most widely adopted data-acquisition configurations in computed tomography (CT). The Feldkamp, Davis, Kress (FDK) algorithm and its various modifications have been developed for reconstructing approximately three-dimensional images from circular cone-beam data. When data contain transverse truncations, however, these algorithms may reconstruct images with significant truncation artifacts. It is of practical significance to develop algorithms that can reconstruct region-of-interest (ROI) images from truncated circular cone-beam data that are free of truncation artifacts and that have an accuracy comparable to that obtained from nontruncated cone-beam data. In this work, we have investigated and developed a backprojection-filtration (BPF)-based algorithm for ROI-image reconstruction from circular cone-beam data containing transverse truncations. Furthermore, we have developed a weighted BPF algorithm to exploit "redundant" information in data for improving image quality. In an effort to validate and evaluate the proposed BPF algorithms for circular cone-beam CT, we have performed numerical studies by using both computer-simulation data and experimental data acquired with a radiotherapy cone-beam CT system. Quantitative results in these studies demonstrate that the proposed BPF algorithms for circular cone-beam CT can reconstruct ROI images free of truncation artifacts.

Region-of-interest reconstruction of motion-contaminated data using a weighted backprojection filtration algorithm

The recently developed weighted backprojection filtration (WBPF) algorithm using data redundancy has capabilities that make this algorithm an attractive candidate for reconstructing images from motion-contaminated projection data. First, the WBPF algorithm is capable of reconstructing region-of-interest (ROI) images from reduced-scan fan-beam data, which have less data than the short-scan data required to reconstruct the entire field of view (FOV). Second, this algorithm can reconstruct ROI images from truncated data. Using phantom simulation studies, we demonstrate how these unique capabilities can be exploited to reduce the amount of motion-contaminated data used for reconstruction. In particular, we use examples from cardiac imaging to illustrate how off-center phantom positioning combined with phase-interval ROI reconstruction can result in the suppression of motion artifacts. In terms of temporal resolution, reduced-scan reconstruction with 45% of a full-scan dataset can be used to improve the temporal resolution of a short-scan reconstruction by 25.8% if ungated data are used. For data gated at 66 beats per minute, reduced-scan reconstruction with 45% of a full-scan dataset can be used to improve the temporal resolution of a short-scan reconstruction by 7.9%. As a result of our studies, we believe that the WBPF algorithm demonstrates the potential for reconstructing quality ROI images from motion-contaminated fan-beam data.

Exact BPF and FBP algorithms for nonstandard saddle curves

A hot topic in cone-beam CT research is exact cone-beam reconstruction from a general scanning trajectory. Particularly, a nonstandard saddle curve attracts attention, as this construct allows the continuous periodic scanning of a volume-of-interest (VOI). Here we evaluate two algorithms for reconstruction from data collected along a nonstandard saddle curve, which are in the filtered backprojection (FBP) and backprojection filtration (BPF) formats, respectively. Both the algorithms are implemented in a chord-based coordinate system. Then, a rebinning procedure is utilized to transform the reconstructed results into the natural coordinate system. The simulation results demonstrate that the FBP algorithm produces better image quality than the BPF algorithm, while both the algorithms exhibit similar noise characteristics.