Exact interior reconstruction from truncated limited-angle projection data

AI-driven projection tomography with multicore fibre-optic cell rotation

Optical tomography has emerged as a non-invasive imaging method, providing three-dimensional insights into subcellular structures and thereby enabling a deeper understanding of cellular functions, interactions, and processes. Conventional optical tomography methods are constrained by a limited illumination scanning range, leading to anisotropic resolution and incomplete imaging of cellular structures. To overcome this problem, we employ a compact multi-core fibre-optic cell rotator system that facilitates precise optical manipulation of cells within a microfluidic chip, achieving full-angle projection tomography with isotropic resolution. Moreover, we demonstrate an AI-driven tomographic reconstruction workflow, which can be a paradigm shift from conventional computational methods, often demanding manual processing, to a fully autonomous process. The performance of the proposed cell rotation tomography approach is validated through the three-dimensional reconstruction of cell phantoms and HL60 human cancer cells. The versatility of this learning-based tomographic reconstruction workflow paves the way for its broad application across diverse tomographic imaging modalities, including but not limited to flow cytometry tomography and acoustic rotation tomography. Therefore, this AI-driven approach can propel advancements in cell biology, aiding in the inception of pioneering therapeutics, and augmenting early-stage cancer diagnostics.

Statistical Interior Tomography via L1 Norm Dictionary Learning without Assuming an Object Support

Interior tomography of X-ray computed tomography (CT) has many advantages, such as a lower radiation dose and lower detector hardware cost compared to traditional CT. However, this imaging technique only uses the projection data passing through the region of interest (ROI) for imaging; accordingly, the projection data are truncated at both ends of the detector, so the traditional analytical reconstruction algorithm cannot satisfy the demand of clinical diagnosis. To solve the above limitations, in this paper we propose a high-quality statistical iterative reconstruction algorithm that uses the zeroth-order image moment as novel prior knowledge; the zeroth-order image moment can be estimated in the projection domain using the Helgason–Ludwig consistency condition. Then, the L1norm of sparse representation, in terms of dictionary learning, and the zeroth-order image moment constraints are incorporated into the statistical iterative reconstruction framework to construct an objective function. Finally, the objective function is minimized using an alternating minimization iterative algorithm. The chest CT image simulated and CT real data experimental results demonstrate that the proposed approach can remove shift artifacts effectively and has superior performance in removing noise and persevering fine structures than the total variation (TV)-based approach.

Global imaging with high resolution region of interest using fusion data based on dual-field of view detection system

X-ray micro-computed tomography (CT) is an important tool for high-resolution three-dimensional imaging. But one limitation of micro-CT is the compromise between resolution and fields of view (FOV). In this paper, we develop an x-rays dual-FOV optical coupling detection (DFOCD) system for global imaging with high-resolution region of interest (ROI). In DFOCD system, the beam splitter separates lights to form two sub-optical paths, two objectives with different FOV and magnification are used in the two sub-optical paths for dual-FOV imaging. Then a data fusion method is proposed to register and fuse dual-FOV data. Reconstructed images are obtained based on back projection filtering algorithm using fusion data. Dual-FOV data are collected simultaneously in DFOCD system, which precludes artifacts in fusion images from phantom movement or changes in two acquisitions on common micro-CT, and also saves scanning time. Simulation and experimental results show that details in ROI and global morphology of phantoms are correctly reconstructed. Bright ring artifacts of ROI caused by truncated data are corrected in reconstruction images. Therefore, global imaging with high-resolution ROI of samples can be obtained by single scan experiment using DFOCD system and data fusion method, which is expected to expand the application of micro-CT.

Clinical validation of CT image reconstruction with interior tomography

Active x-ray collimation is well adopted in radiography and fluoroscopy for radiation dose reduction and image quality improvement. The application of this concept in computed tomography (CT) is significantly limited due to the truncation of projection data. Generally, an internal field of view (FOV) inside an imaging object cannot be exactly reconstructed only from the truncated projection data. Recent research shows that given some prior information of the FOV image, interior tomography can provide a unique and stable solution for image reconstruction of an internal FOV. The objective of this study is to evaluate the performance of interior reconstruction based on patient datasets obtained from a clinical CT scanner with dual x-ray tubes, which simultaneously gives full projections and truncated projections. Image reconstructions are performed from full and truncated projection data for the comparison of image quality, respectively. The reconstructed CT images were reviewed by a radiologist and a resident. The evaluation results of two observers showed that CT images reconstructed with truncated projections met clinically diagnostic requirements and were comparable to clinical images. This study demonstrates that with the development of interior tomography, active x-ray collimation in the imaging plane can be readily employed in CT imaging to further reduce patient radiation and improve image quality.

Quest for the ultimate cardiac CT scanner

PURPOSE

To quantitatively evaluate and compare six proposed system architectures for cardiac CT scanning.

METHODS

Starting from the clinical requirements for cardiac CT, we defined six dedicated cardiac CT architectures. We selected these architectures based on a previous screening study and defined them in sufficient detail to comprehensively analyze their cost and performance. We developed rigorous comparative evaluation methods for the most important aspects of performance and cost, and we applied these evaluation criteria to the defined cardiac CT architectures.

RESULTS

We found that CT system architectures based on the third-generation geometry provide nearly linear performance improvement versus the increased cost of additional beam lines (i.e., source-detector pairs), although similar performance improvement could be achieved with advanced motion-correction algorithms. The third-generation architectures outperform even the most promising of the proposed architectures that deviate substantially from the traditional CT system architectures.

CONCLUSION

This work confirms the validity of the current trend in commercial CT scanner design. However, we anticipate that over time, CT hardware and software technologies will evolve, the relative importance of the performance criteria will change, the relative costs of components will vary, some of the remaining challenges will be addressed, and perhaps new candidate architectures will be identified; therefore, the conclusion of a comparative analysis like this may change. The evaluation methods that we used can provide a framework for other researchers to analyze their own proposed CT architectures.

Interior tomography with curvelet-based regularization

The interior problem, i.e. reconstruction from local truncated projections in computed tomography (CT), is common in practical applications. However, its solution is non-unique in a general unconstrained setting. To solve the interior problem uniquely and stably, in recent years both the prior knowledge- and compressive sensing (CS)-based methods have been developed. Those theoretically exact solutions for the interior problem are called interior tomography. Along this direction, we propose here a new CS-based method for the interior problem based on the curvelet transform. A curvelet is localized in both radial and angular directions in the frequency domain. A two-dimensional (2D) image can be represented in a curvelet frame. We employ the curvelet transform coefficients to regularize the interior problem and obtain a curvelet frame based regularization method (CFRM) for interior tomography. The curvelet coefficients of the reconstructed image are split into two sets according to their visibility from the interior data, and different regularization parameters are used for these two sets. We also presents the results of numerical experiments, which demonstrate the feasibility of the proposed approach.

An adaptive reconstruction algorithm for spectral CT regularized by a reference image

The photon counting detector based spectral CT system is attracting increasing attention in the CT field. However, the spectral CT is still premature in terms of both hardware and software. To reconstruct high quality spectral images from low-dose projections, an adaptive image reconstruction algorithm is proposed that assumes a known reference image (RI). The idea is motivated by the fact that the reconstructed images from different spectral channels are highly correlated. If a high quality image of the same object is known, it can be used to improve the low-dose reconstruction of each individual channel. This is implemented by maximizing the patch-wise correlation between the object image and the RI. Extensive numerical simulations and preclinical mouse study demonstrate the feasibility and merits of the proposed algorithm. It also performs well for truncated local projections, and the surrounding area of the region- of-interest (ROI) can be more accurately reconstructed. Furthermore, a method is introduced to adaptively choose the step length, making the algorithm more feasible and easier for applications.

A spectral interior CT by a framelet-based reconstruction algorithm

Reducing radiation dose is an important goal in medical computed tomography (CT), for which interior tomography is an effective approach. There have been interior reconstruction algorithms for monochromatic CT, but in reality, X-ray sources are polychromatic. Using a polychromatic acquisition model and motivated by framelet-based image processing algorithms, in this paper, we propose an interior reconstruction algorithm to obtain an image with spectral information assuming only one scan with a current energy-integrating detector. This algorithm is a new nonlinear iterative method by minimizing a special functional under a polychromatic acquisition model for X-ray CT, where the attenuation coefficients are energy-dependent. Experimental results validate that our algorithm can effectively reduce the beam-hardening artifacts and metal artifacts. It also produces color overlays which are useful in tumor identification and quantification.

Cardiac CT: A system architecture study

BACKGROUND

We are interested in exploring dedicated, high-performance cardiac CT systems optimized to provide the best tradeoff between system cost, image quality, and radiation dose.

OBJECTIVE

We sought to identify and evaluate a broad range of CT architectures that could provide an optimal, dedicated cardiac CT solution.

METHODS

We identified and evaluated thirty candidate architectures using consistent design choices. We defined specific evaluation metrics related to cost and performance. We then scored the candidates versus the defined metrics. Lastly, we applied a weighting system to combine scores for all metrics into a single overall score for each architecture. CT experts with backgrounds in cardiovascular radiology, x-ray physics, CT hardware and CT algorithms performed the scoring and weighting.

RESULTS

We found nearly a twofold difference between the most and the least promising candidate architectures. Architectures employed by contemporary commercial diagnostic CT systems were among the highest-scoring candidates. We identified six architectures that show sufficient promise to merit further in-depth analysis and comparison.

CONCLUSION

Our results suggest that contemporary diagnostic CT system architectures outperform most other candidates that we evaluated, but the results for a few alternatives were relatively close. We selected six representative high-scoring candidates for more detailed design and further comparative evaluation.

Patient-bounded extrapolation using low-dose priors for volume-of-interest imaging in C-arm CT

PURPOSE

Three-dimensional (3D) volume-of-interest (VOI) imaging with C-arm systems provides anatomical information in a predefined 3D target region at a considerably low x-ray dose. However, VOI imaging involves laterally truncated projections from which conventional reconstruction algorithms generally yield images with severe truncation artifacts. Heuristic based extrapolation methods, e.g., water cylinder extrapolation, typically rely on techniques that complete the truncated data by means of a continuity assumption and thus appear to be ad-hoc. It is our goal to improve the image quality of VOI imaging by exploiting existing patient-specific prior information in the workflow.

METHODS

A necessary initial step prior to a 3D acquisition is to isocenter the patient with respect to the target to be scanned. To this end, low-dose fluoroscopic x-ray acquisitions are usually applied from anterior-posterior (AP) and medio-lateral (ML) views. Based on this, the patient is isocentered by repositioning the table. In this work, we present a patient-bounded extrapolation method that makes use of these noncollimated fluoroscopic images to improve image quality in 3D VOI reconstruction. The algorithm first extracts the 2D patient contours from the noncollimated AP and ML fluoroscopic images. These 2D contours are then combined to estimate a volumetric model of the patient. Forward-projecting the shape of the model at the eventually acquired C-arm rotation views gives the patient boundary information in the projection domain. In this manner, we are in the position to substantially improve image quality by enforcing the extrapolated line profiles to end at the known patient boundaries, derived from the 3D shape model estimate.

RESULTS

The proposed method was evaluated on eight clinical datasets with different degrees of truncation. The proposed algorithm achieved a relative root mean square error (rRMSE) of about 1.0% with respect to the reference reconstruction on nontruncated data, even in the presence of severe truncation, compared to a rRMSE of 8.0% when applying a state-of-the-art heuristic extrapolation technique.

CONCLUSIONS

The method we proposed in this paper leads to a major improvement in image quality for 3D C-arm based VOI imaging. It involves no additional radiation when using fluoroscopic images that are acquired during the patient isocentering process. The model estimation can be readily integrated into the existing interventional workflow without additional hardware.

Towards clinical application of a Laplace operator-based region of interest reconstruction algorithm in C-arm CT

It is known that a reduction of the field-of-view in 3-D X-ray imaging is proportional to a reduction in radiation dose. The resulting truncation, however, is incompatible with conventional reconstruction algorithms. Recently, a novel method for region of interest reconstruction that uses neither prior knowledge nor extrapolation has been published, named approximated truncation robust algorithm for computed tomography (ATRACT). It is based on a decomposition of the standard ramp filter into a 2-D Laplace filtering and a 2-D Radon-based residual filtering step. In this paper, we present two variants of the original ATRACT. One is based on expressing the residual filter as an efficient 2-D convolution with an analytically derived kernel. The second variant is to apply ATRACT in 1-D to further reduce computational complexity. The proposed algorithms were evaluated by using a reconstruction benchmark, as well as two clinical data sets. The results are encouraging since the proposed algorithms achieve a speed-up factor of up to 245 compared to the 2-D Radon-based ATRACT. Reconstructions of high accuracy are obtained, e.g., even real-data reconstruction in the presence of severe truncation achieve a relative root mean square error of as little as 0.92% with respect to nontruncated data.

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.

The meaning of interior tomography

The classic imaging geometry for computed tomography is for the collection of un-truncated projections and the reconstruction of a global image, with the Fourier transform as the theoretical foundation that is intrinsically non-local. Recently, interior tomography research has led to theoretically exact relationships between localities in the projection and image spaces and practically promising reconstruction algorithms. Initially, interior tomography was developed for x-ray computed tomography. Then, it was elevated to have the status of a general imaging principle. Finally, a novel framework known as 'omni-tomography' is being developed for a grand fusion of multiple imaging modalities, allowing tomographic synchrony of diversified features.

Image reconstruction for sparse-view CT and interior CT-introduction to compressed sensing and differentiated backprojection

New designs of future computed tomography (CT) scanners called sparse-view CT and interior CT have been considered in the CT community. Since these CTs measure only incomplete projection data, a key to put these CT scanners to practical use is a development of advanced image reconstruction methods. After 2000, there was a large progress in this research area briefly summarized as follows. In the sparse-view CT, various image reconstruction methods using the compressed sensing (CS) framework have been developed towards reconstructing clinically feasible images from a reduced number of projection data. In the interior CT, several novel theoretical results on solution uniqueness and solution stability have been obtained thanks to the discovery of a new class of reconstruction methods called differentiated backprojection (DBP). In this paper, we mainly review this progress including mathematical principles of the CS image reconstruction and the DBP image reconstruction for readers unfamiliar with this area. We also show some experimental results from our past research to demonstrate that this progress is not only theoretically elegant but also works in practical imaging situations.

Time-resolved cardiac interventional cone-beam CT reconstruction from fully truncated projections using the prior image constrained compressed sensing (PICCS) algorithm

C-arm cone-beam CT could replace preoperative multi-detector CT scans in the cardiac interventional setting. However, cardiac gating results in view angle undersampling and the small size of the detector results in projection data truncation. These problems are incompatible with conventional tomographic reconstruction algorithms. In this paper, the prior image constrained compressed sensing (PICCS) reconstruction method was adapted to solve these issues. The performance of the proposed method was compared to that of FDK, FDK with extrapolated projection data (E-FDK), and total variation-based compressed sensing. A canine projection dataset acquired using a clinical C-arm imaging system supplied realistic cardiac motion and anatomy for this evaluation. Three different levels of truncation were simulated. The relative root mean squared error and the universal image quality index were used to quantify the reconstruction accuracy. Three main conclusions were reached. (1) The adapted version of the PICCS algorithm offered the highest image quality and reconstruction accuracy. (2) No meaningful variation in performance was observed when the amount of truncation was changed. (3) This study showed evidence that accurate interior tomography with an undersampled acquisition is possible for realistic objects if a prior image with minimal artifacts is available.

Completeness map evaluation demonstrated with candidate next-generation cardiac CT architectures

PURPOSE

In this report, the authors introduce the general concept of the completeness map, as a means to evaluate the completeness of data acquired by a given CT system design (architecture and scan mode). They illustrate the utility of completeness map by applying the completeness map concept to a number of candidate CT system designs, as part of a study to advance the state-of-the-art in cardiac CT.

METHODS

In order to optimally reconstruct a point within a volume of interest (VOI), the Radon transform on all possible planes through that point should be measured. The authors quantified the extent to which this ideal condition is satisfied for the entire image volume. They first determined a Radon completeness number for each point in the VOI, as the percentage of possible planes that is actually measured. A completeness map is then defined as a 3D matrix of the completeness numbers for the entire VOI. The authors proposed algorithms to analyze the projection datasets in Radon space and compute the completeness number for a fixed point and apply these algorithms to various architectures and scan modes that they are evaluating. In this report, the authors consider four selected candidate architectures, operating with different scan modes, for a total of five system design alternatives. Each of these alternatives is evaluated using completeness map.

RESULTS

If the detector size and cone angle are large enough to cover the entire cardiac VOI, a single-source circular scan can have ≥99% completeness over the entire VOI. However, only the central z-slice can be exactly reconstructed, which corresponds to 100% completeness. For a typical single-source architecture, if the detector is limited to an axial dimension of 40 mm, a helical scan needs about five rotations to form an exact reconstruction region covering the cardiac VOI, while a triple-source helical scan only requires two rotations, leading to a 2.5x improvement in temporal resolution. If the source and detector of an inverse-geometry (IGCT) system have the same axial extent, and the spacing of source points in the axial and transaxial directions is sufficiently small, the IGCT can also form an exact reconstruction region for the cardiac VOI. If the VOI can be covered by the x-ray beam in any view, a composite-circling scan can generate an exact reconstruction region covering the VOI.

CONCLUSIONS

The completeness map evaluation provides useful information for selecting the next-generation cardiac CT system design. The proposed completeness map method provides a practical tool for analyzing complex scanning trajectories, where the theoretical image quality for some complex system designs is impossible to predict, without yet-undeveloped reconstruction algorithms.

Image reconstruction for hybrid true-color micro-CT

X-ray micro-CT is an important imaging tool for biomedical researchers. Our group has recently proposed a hybrid "true-color" micro-CT system to improve contrast resolution with lower system cost and radiation dose. The system incorporates an energy-resolved photon-counting true-color detector into a conventional micro-CT configuration, and can be used for material decomposition. In this paper, we demonstrate an interior color-CT image reconstruction algorithm developed for this hybrid true-color micro-CT system. A compressive sensing-based statistical interior tomography method is employed to reconstruct each channel in the local spectral imaging chain, where the reconstructed global gray-scale image from the conventional imaging chain served as the initial guess. Principal component analysis was used to map the spectral reconstructions into the color space. The proposed algorithm was evaluated by numerical simulations, physical phantom experiments, and animal studies. The results confirm the merits of the proposed algorithm, and demonstrate the feasibility of the hybrid true-color micro-CT system. Additionally, a "color diffusion" phenomenon was observed whereby high-quality true-color images are produced not only inside the region of interest, but also in neighboring regions. It appears harnessing that this phenomenon could potentially reduce the color detector size for a given ROI, further reducing system cost and radiation dose.

High-order total variation minimization for interior SPECT

Recently, we developed an approach for solving the computed tomography (CT) interior problem based on the high-order TV (HOT) minimization, assuming that a region-of-interest (ROI) is piecewise polynomial. In this paper, we generalize this finding from the CT field to the single-photon emission computed tomography (SPECT) field, and prove that if an ROI is piecewise polynomial, then the ROI can be uniquely reconstructed from the SPECT projection data associated with the ROI through the HOT minimization. Also, we propose a new formulation of HOT, which has an explicit formula for any n-order piecewise polynomial function, while the original formulation has no explicit formula for n ≥ 2. Finally, we verify our theoretical results in numerical simulation, and discuss relevant issues.

STABILITY OF THE INTERIOR PROBLEM FOR POLYNOMIAL REGION OF INTEREST

In many practical applications, it is desirable to solve the interior problem of tomography without requiring knowledge of the attenuation function f_a on an open set within the region of interest (ROI). It was proved recently that the interior problem has a unique solution if f_a is assumed to be piecewise polynomial on the ROI. In this paper, we tackle the related question of stability. It is well-known that lambda tomography allows one to stably recover the locations and values of the jumps of f_a inside the ROI from only the local data. Hence, we consider here only the case of a polynomial, rather than piecewise polynomial, f_a on the ROI. Assuming that the degree of the polynomial is known, along with some other fairly mild assumptions on f_a , we prove a stability estimate for the interior problem. Additionally, we prove the following general uniqueness result. If there is an open set U on which f_a is the restriction of a real-analytic function, then f_a is uniquely determined by only the line integrals through U. It turns out that two known uniqueness theorems are corollaries of this result.

Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM)

We propose a compressive sensing approach for multi-energy computed tomography (CT), namely the prior rank, intensity and sparsity model (PRISM). To further compress the multi-energy image for allowing the reconstruction with fewer CT data and less radiation dose, the PRISM models a multi-energy image as the superposition of a low-rank matrix and a sparse matrix (with row dimension in space and column dimension in energy), where the low-rank matrix corresponds to the stationary background over energy that has a low matrix rank, and the sparse matrix represents the rest of distinct spectral features that are often sparse. Distinct from previous methods, the PRISM utilizes the generalized rank, e.g., the matrix rank of tight-frame transform of a multi-energy image, which offers a way to characterize the multi-level and multi-filtered image coherence across the energy spectrum. Besides, the energy-dependent intensity information can be incorporated into the PRISM in terms of the spectral curves for base materials, with which the restoration of the multi-energy image becomes the reconstruction of the energy-independent material composition matrix. In other words, the PRISM utilizes prior knowledge on the generalized rank and sparsity of a multi-energy image, and intensity/spectral characteristics of base materials. Furthermore, we develop an accurate and fast split Bregman method for the PRISM and demonstrate the superior performance of the PRISM relative to several competing methods in simulations.

Compressive sensing-based interior tomography: preliminary clinical application

Compressive sensing (CS)-based interior tomography is a state-of-the-art method for accurate image reconstruction from only locally truncated projections. Here, we report our preliminary interior tomography results reconstructed from raw projections of a patient acquired on a GE Discovery CT750 HD scanner. This is the first clinical application of the CS-based interior reconstruction techniques, and the results show an excellent match with those reconstructed from global projections.

Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems

A multisource x-ray interior imaging system with limited angle scanning is investigated to study the possibility of building an ultrafast micro-CT for dynamic small animal imaging, and two methods are employed to perform interior reconstruction from a limited number of projections collected by the multisource interior x-ray system. The first is total variation minimization with the steepest descent search (TVM-SD) and the second is total difference minimization with soft-threshold filtering (TDM-STF). Comprehensive numerical simulations and animal studies are performed to validate the associated reconstructed methods and demonstrate the feasibility and application of the proposed system configuration. The image reconstruction results show that both of the two reconstruction methods can significantly improve the image quality and the TDM-SFT is slightly superior to the TVM-SD. Finally, quantitative image analysis shows that it is possible to make an ultrafast micro-CT using a multisource interior x-ray system scheme combined with the state-of-the-art interior tomography.

Short echo-time 3D radial gradient-echo MRI using concurrent dephasing and excitation

Ultrashort echo-time imaging and sweep imaging with Fourier transformation are powerful techniques developed for imaging ultrashort T(2) species. However, it can be challenging to implement them on standard clinical MRI systems due to demanding hardware requirements. In this article, the limits of what is possible in terms of the minimum echo-time and repetition time with 3D radial gradient-echo sequences, which can be readily implemented on a standard clinical scanner, are investigated. Additionally, a new 3D radial gradient-echo sequence is introduced, called COncurrent Dephasing and Excitation (CODE). The unique feature of CODE is that the initial dephasing of the readout gradient is performed during RF excitation, which allows CODE to effectively achieve echo-times on the order of ∼0.2 ms and larger in a clinical setting. The minimum echo-time achievable with CODE is analytically described and compared with a standard 3D radial gradient-echo sequence. CODE was implemented on a clinical 3 T scanner (Siemens 3 T MAGNETOM Trio), and both phantom and in vivo human knee images are shown for demonstration.

Robust principal component analysis-based four-dimensional computed tomography

The purpose of this paper for four-dimensional (4D) computed tomography (CT) is threefold. (1) A new spatiotemporal model is presented from the matrix perspective with the row dimension in space and the column dimension in time, namely the robust PCA (principal component analysis)-based 4D CT model. That is, instead of viewing the 4D object as a temporal collection of three-dimensional (3D) images and looking for local coherence in time or space independently, we perceive it as a mixture of low-rank matrix and sparse matrix to explore the maximum temporal coherence of the spatial structure among phases. Here the low-rank matrix corresponds to the 'background' or reference state, which is stationary over time or similar in structure; the sparse matrix stands for the 'motion' or time-varying component, e.g., heart motion in cardiac imaging, which is often either approximately sparse itself or can be sparsified in the proper basis. Besides 4D CT, this robust PCA-based 4D CT model should be applicable in other imaging problems for motion reduction or/and change detection with the least amount of data, such as multi-energy CT, cardiac MRI, and hyperspectral imaging. (2) A dynamic strategy for data acquisition, i.e. a temporally spiral scheme, is proposed that can potentially maintain similar reconstruction accuracy with far fewer projections of the data. The key point of this dynamic scheme is to reduce the total number of measurements, and hence the radiation dose, by acquiring complementary data in different phases while reducing redundant measurements of the common background structure. (3) An accurate, efficient, yet simple-to-implement algorithm based on the split Bregman method is developed for solving the model problem with sparse representation in tight frames.

Statistical interior tomography

This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize the objective function with an initial image from the direct inversion of the truncated Hilbert transform. The proposed SIT approach is extensively evaluated with both numerical and real datasets. The results demonstrate that SIT is robust with respect to data noise and down-sampling, and has better resolution and less bias than its deterministic counterpart in the case of low count data.

Exact iterative reconstruction for the interior problem

There is a trend in single photon emission computed tomography (SPECT) that small and dedicated imaging systems are becoming popular. For example, many companies are developing small dedicated cardiac SPECT systems with different designs. These dedicated systems have a smaller field of view (FOV) than a full-size clinical system. Thus data truncation has become the norm rather than the exception in these systems. Therefore, it is important to develop region of interest (ROI) reconstruction algorithms using truncated data. This paper is a stepping stone toward this direction. This paper shows that the common generic iterative image reconstruction algorithms are able to exactly reconstruct the ROI under the conditions that the convex ROI is fully sampled and the image value in a sub-region within the ROI is known. If the ROI includes a sub-region that is outside the patient body, then the conditions can be easily satisfied.

Interior SPECT- Exact and Stable ROI Reconstruction from Uniformly Attenuated Local Projections

Single photon emission computed tomography (SPECT) is an important biomedical imaging modality. However, since gamma cameras are expensive and bulky, truncated projection data are either preferred or unavoidable. Inspired by the recent results on interior tomography in the x-ray CT field, here we present the interior SPECT approach for exact and stable reconstruction of a region of interest (ROI) from uniformly attenuated local projection data, aided by prior knowledge of a sub-region in the ROI. First, by analytic continuation we prove that interior SPECT is both exact and stable, and by singular value decomposition (SVD) we establish the stability of interior SPECT. Then, given the constant attenuation coefficient and object boundary, our interior SPECT reconstruction is achieved by inverting a generalized truncated Hilbert transform using the SVD technique. Preliminary numerical simulation data demonstrate that our work has practical utilities. The theoretical generalization of our work to the variable attenuation case is underway, and the same numerical approach can be applied.

Compressed sensing based interior tomography

While conventional wisdom is that the interior problem does not have a unique solution, by analytic continuation we recently showed that the interior problem can be uniquely and stably solved if we have a known sub-region inside a region of interest (ROI). However, such a known sub-region is not always readily available, and it is even impossible to find in some cases. Based on compressed sensing theory, here we prove that if an object under reconstruction is essentially piecewise constant, a local ROI can be exactly and stably reconstructed via the total variation minimization. Because many objects in computed tomography (CT) applications can be approximately modeled as piecewise constant, our approach is practically useful and suggests a new research direction for interior tomography. To illustrate the merits of our finding, we develop an iterative interior reconstruction algorithm that minimizes the total variation of a reconstructed image and evaluate the performance in numerical simulation.

A filtered backprojection algorithm for triple-source helical cone-beam CT

Multisource cone-beam computed tomography (CT) is an attractive approach of choice for superior temporal resolution, which is critically important for cardiac imaging and contrast enhanced studies. In this paper, we present a filtered-backprojection (FBP) algorithm for triple-source helical cone-beam CT. The algorithm is both exact and efficient. It utilizes data from three inter-helix PI-arcs associated with the inter-helix PI-lines and the minimum detection windows defined for the triple-source configuration. The proof of the formula is based on the geometric relations specific to triple-source helical cone-beam scanning. Simulation results demonstrate the validity of the reconstruction algorithm. This algorithm is also extended to a multisource version for (2N + 1)-source helical cone-beam CT. With parallel computing, the proposed FBP algorithms can be significantly faster than our previously published multisource backprojection-filtration algorithms. Thus, the FBP algorithms are promising in applications of triple-source helical cone-beam CT.

Compressive sampling based interior reconstruction for dynamic carbon nanotube micro-CT

In the computed tomography (CT) field, one recent invention is the so-called carbon nanotube (CNT) based field emission x-ray technology. On the other hand, compressive sampling (CS) based interior tomography is a new innovation. Combining the strengths of these two novel subjects, we apply the interior tomography technique to local mouse cardiac imaging using respiration and cardiac gating with a CNT based micro-CT scanner. The major features of our method are: (1) it does not need exact prior knowledge inside an ROI; and (2) two orthogonal scout projections are employed to regularize the reconstruction. Both numerical simulations and in vivo mouse studies are performed to demonstrate the feasibility of our methodology.