A fast regularized iterative algorithm for fan-beam CT reconstruction

We propose a fast iterative image reconstruction algorithm for normal, short-scan, and super-short-scan fan-beam computed tomography (CT), which aims at iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with a total variation (TV) penalty. The derivation of the algorithm can be outlined as follows. First, the original minimization problem is formulated into a saddle-point (primal-dual) problem by using the Lagrangian duality, to which we apply the alternating projection proximal (APP) algorithm, which belongs to a class of first-order primal-dual methods. Second, we precondition the iterative formula using the modified ramp filter of the filtered back-projection (FBP) reconstruction algorithm in such a way that the solution to this preconditioned iteration perfectly coincides with the solution to the original problem. The resulting algorithm converges quickly to the minimizer of the cost function. To demonstrate the advantages of our method, we perform reconstruction experiments using projection data from both numerical phantoms and real CT data. Both qualitative and quantitative results are presented.

Fourier-Domain Analysis of the Iterative Landweber Algorithm

This paper proposes a novel method of using the frequency-domain transfer function to investigate the property of an iterative algorithm for minimizing a quadratic objective function. This paper focuses on a two-dimensional (2D) tomography problem, which can be X-ray computed tomography (CT), positron emission tomography (PET), and single photon emission computed tomography (SPECT). Two questions regarding to the linear iterative Landweber algorithm are considered. The first question is whether stopping early is equivalent to getting a minimum-norm solution. The second question is whether the low frequency components always converge first. Our answers to these two questions are No.

Image quality, diagnostic accuracy, and potential for radiation dose reduction in thoracoabdominal CT, using Sinogram Affirmed Iterative Reconstruction (SAFIRE) technique in a longitudinal study

Objective

To step-wise evaluate image quality of sinogram-affirmed iterative reconstruction (SAFIRE) in reduced-dose (RD) thoracoabdominal computed tomography (CT) compared to full-dose (FD) and RD filtered back projection (FBP) in a longitudinal study.

Materials and methods

122 patients were included in this prospective study. 49 patients (14 men: mean age ± SD, 56±0.4 years; 35 women: 58±1.3 years) completed FD, RD1 (80%-dose) and RD2 (60%-dose) thoracoabdominal CT. Each CT dataset was reconstructed with FBP and SAFIRE. For quantitative image analysis image noise was measured in defined tissue regions. Qualitative image evaluation was performed according to the European Guidelines on Quality criteria for CT. Additionally artifacts, lesion conspicuity, and edge sharpness were assessed.

Results

Compared to FD-FBP noise in soft tissue increased by 12% in RD1-FBP and 27% in RD2-FBP reconstructions, whereas SAFIRE lead to a decrease of 28% (RD1) and 17% (RD2), respectively (all p <0.001). Visually sharp reproduction, lesion conspicuity, edge sharpness of pathologic findings, and overall image quality did not differ statistically significant between FD-FBP and RD-SAFIRE datasets. Image quality decreased in RD1- and RD2-FBP compared to FD-FBP, reaching statistically significance in RD2 datasets (p <0.001). In RD1- and RD2-FBP (p <0.001) streak artifacts were noted.

Conclusion

Using SAFIRE the reference mAs in thoracoabdominal CT can be reduced by at least 30% in clinical routine without loss of image quality or diagnostic information.

A comparison of linear interpolation models for iterative CT reconstruction

PURPOSE

Recent reports indicate that model-based iterative reconstruction methods may improve image quality in computed tomography (CT). One difficulty with these methods is the number of options available to implement them, including the selection of the forward projection model and the penalty term. Currently, the literature is fairly scarce in terms of guidance regarding this selection step, whereas these options impact image quality. Here, the authors investigate the merits of three forward projection models that rely on linear interpolation: the distance-driven method, Joseph's method, and the bilinear method. The authors' selection is motivated by three factors: (1) in CT, linear interpolation is often seen as a suitable trade-off between discretization errors and computational cost, (2) the first two methods are popular with manufacturers, and (3) the third method enables assessing the importance of a key assumption in the other methods.

METHODS

One approach to evaluate forward projection models is to inspect their effect on discretized images, as well as the effect of their transpose on data sets, but significance of such studies is unclear since the matrix and its transpose are always jointly used in iterative reconstruction. Another approach is to investigate the models in the context they are used, i.e., together with statistical weights and a penalty term. Unfortunately, this approach requires the selection of a preferred objective function and does not provide clear information on features that are intrinsic to the model. The authors adopted the following two-stage methodology. First, the authors analyze images that progressively include components of the singular value decomposition of the model in a reconstructed image without statistical weights and penalty term. Next, the authors examine the impact of weights and penalty on observed differences.

RESULTS

Image quality metrics were investigated for 16 different fan-beam imaging scenarios that enabled probing various aspects of all models. The metrics include a surrogate for computational cost, as well as bias, noise, and an estimation task, all at matched resolution. The analysis revealed fundamental differences in terms of both bias and noise. Task-based assessment appears to be required to appreciate the differences in noise; the estimation task the authors selected showed that these differences balance out to yield similar performance. Some scenarios highlighted merits for the distance-driven method in terms of bias but with an increase in computational cost. Three combinations of statistical weights and penalty term showed that the observed differences remain the same, but strong edge-preserving penalty can dramatically reduce the magnitude of these differences.

CONCLUSIONS

In many scenarios, Joseph's method seems to offer an interesting compromise between cost and computational effort. The distance-driven method offers the possibility to reduce bias but with an increase in computational cost. The bilinear method indicated that a key assumption in the other two methods is highly robust. Last, strong edge-preserving penalty can act as a compensator for insufficiencies in the forward projection model, bringing all models to similar levels in the most challenging imaging scenarios. Also, the authors find that their evaluation methodology helps appreciating how model, statistical weights, and penalty term interplay together.

Mixed Confidence Estimation for Iterative CT Reconstruction

Dynamic (4D) CT imaging is used in a variety of applications, but the two major drawbacks of the technique are its increased radiation dose and longer reconstruction time. Here we present a statistical analysis of our previously proposed Mixed Confidence Estimation (MCE) method that addresses both these issues. This method, where framed iterative reconstruction is only performed on the dynamic regions of each frame while static regions are fixed across frames to a composite image, was proposed to reduce computation time. In this work, we generalize the previous method to describe any application where a portion of the image is known with higher confidence (static, composite, lower-frequency content, etc.) and a portion of the image is known with lower confidence (dynamic, targeted, etc). We show that by splitting the image space into higher and lower confidence components, MCE can lower the estimator variance in both regions compared to conventional reconstruction. We present a theoretical argument for this reduction in estimator variance and verify this argument with proof-of-principle simulations. We also propose a fast approximation of the variance of images reconstructed with MCE and confirm that this approximation is accurate compared to analytic calculations of and multi-realization image variance. This MCE method requires less computation time and provides reduced image variance for imaging scenarios where portions of the image are known with more certainty than others allowing for potentially reduced radiation dose and/or improved dynamic imaging.

Regularized Iterative Weighted Filtered Back-Projection for Few-View Data Photoacoustic Imaging

Photoacoustic imaging is an emerging noninvasive imaging technique with great potential for a wide range of biomedical imaging applications. However, with few-view data the filtered back-projection method will create streak artifacts. In this study, the regularized iterative weighted filtered back-projection method was applied to our photoacoustic imaging of the optical absorption in phantom from few-view data. This method is based on iterative application of a nonexact 2DFBP. By adding a regularization operation in the iterative loop, the streak artifacts have been reduced to a great extent and the convergence properties of the iterative scheme have been improved. Results of numerical simulations demonstrated that the proposed method was superior to the iterative FBP method in terms of both accuracy and robustness to noise. The quantitative image evaluation studies have shown that the proposed method outperforms conventional iterative methods.

Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography

PURPOSE

This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing.

METHODS

The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ0 pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD.

RESULTS

The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks.

CONCLUSIONS

A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.

Task-based image quality evaluation of iterative reconstruction methods for low dose CT using computer simulations

Iterative reconstruction (IR) methods for x-ray CT is a promising approach to improve image quality or reduce radiation dose to patients. The goal of this work was to use task based image quality measures and the channelized Hotelling observer (CHO) to evaluate both analytic and IR methods for clinical x-ray CT applications. We performed realistic computer simulations at five radiation dose levels, from a clinical reference low dose D0 to 25% D0. A fixed size and contrast lesion was inserted at different locations into the liver of the XCAT phantom to simulate a weak signal. The simulated data were reconstructed on a commercial CT scanner (SOMATOM Definition Flash; Siemens, Forchheim, Germany) using the vendor-provided analytic (WFBP) and IR (SAFIRE) methods. The reconstructed images were analyzed by CHOs with both rotationally symmetric (RS) and rotationally oriented (RO) channels, and with different numbers of lesion locations (5, 10, and 20) in a signal known exactly (SKE), background known exactly but variable (BKEV) detection task. The area under the receiver operating characteristic curve (AUC) was used as a summary measure to compare the IR and analytic methods; the AUC was also used as the equal performance criterion to derive the potential dose reduction factor of IR. In general, there was a good agreement in the relative AUC values of different reconstruction methods using CHOs with RS and RO channels, although the CHO with RO channels achieved higher AUCs than RS channels. The improvement of IR over analytic methods depends on the dose level. The reference dose level D0 was based on a clinical low dose protocol, lower than the standard dose due to the use of IR methods. At 75% D0, the performance improvement was statistically significant (p < 0.05). The potential dose reduction factor also depended on the detection task. For the SKE/BKEV task involving 10 lesion locations, a dose reduction of at least 25% from D0 was achieved.

Deformable image registration of CT and truncated cone-beam CT for adaptive radiation therapy

Truncation of a cone-beam computed tomography (CBCT) image, mainly caused by the limited field of view (FOV) of CBCT imaging, poses challenges to the problem of deformable image registration (DIR) between computed tomography (CT) and CBCT images in adaptive radiation therapy (ART). The missing information outside the CBCT FOV usually causes incorrect deformations when a conventional DIR algorithm is utilized, which may introduce significant errors in subsequent operations such as dose calculation. In this paper, based on the observation that the missing information in the CBCT image domain does exist in the projection image domain, we propose to solve this problem by developing a hybrid deformation/reconstruction algorithm. As opposed to deforming the CT image to match the truncated CBCT image, the CT image is deformed such that its projections match all the corresponding projection images for the CBCT image. An iterative forward-backward projection algorithm is developed. Six head-and-neck cancer patient cases are used to evaluate our algorithm, five with simulated truncation and one with real truncation. It is found that our method can accurately register the CT image to the truncated CBCT image and is robust against image truncation when the portion of the truncated image is less than 40% of the total image.

CT enterography at 80 kVp with adaptive statistical iterative reconstruction versus at 120 kVp with standard reconstruction: image quality, diagnostic adequacy, and dose reduction

OBJECTIVE

The objective of our study was to evaluate the image quality and diagnostic adequacy of the following two CT enterography protocols in patients weighing less than 160 lb (72 kg): 80-kVp imaging with the adaptive statistical iterative reconstruction (ASIR) in comparison with 120-kVp imaging with the filtered back projection reconstruction.

MATERIALS AND METHODS

We retrospectively reviewed 133 CT enterography examinations of 127 patients weighing less than 160 lb, 64 80-kVp examinations, and 69 120-kVp examinations. Image quality for evaluation of the bowel wall, mesenteric vessels, and hepatic parenchyma and the overall image quality were graded on a scale of 1-5 (1 = poor, 2 = acceptable, 3 = good, 4 = very good, 5 = excellent). Diagnostic accuracy for the detection of inflammatory bowel disease was evaluated. The volume CT dose index (CTDI(vol)) was recorded and effective dose was calculated from scanner-generated dose-length product.

RESULTS

There was a statistically significant decrease in the mean image quality scores for 80-kVp examinations compared with 120-kVp examinations for evaluation of the bowel wall (3.19 vs 3.70, respectively) and liver (3.12 vs 3.81) and for overall image quality (3.23 vs 3.68), but there was no significant decrease in score for evaluation of the mesenteric vessels (3.63 vs 3.67). None of the 80-kVp examinations was graded as poor, and all were considered to be of acceptable quality. Both techniques had comparable diagnostic accuracy for the detection of inflammatory bowel disease. Interobserver agreement was fair to moderate for qualitative image grading and was substantial for the detection of features of inflammatory bowel disease. The mean CTDI(vol) and effective dose for the 80-kVp examinations were 6.15 mGy and 4.60 mSv, respectively, and for the 120-kVp examinations, 20.79 mGy and 15.81 mSv.

CONCLUSION

In patients weighing less than 160 lb, CT enterography examinations at 80 kVp with 30% ASIR produce diagnostically acceptable image quality with an average CTDI(vol) of 6.15 mGy and an average effective dose of 4.60 mSv.

A comparison of reconstruction and viewing parameters on image quality and accuracy of stress myocardial CT perfusion

BACKGROUND

Myocardial stress computed tomography perfusion (CTP) has similar diagnostic accuracy for detecting perfusion defects (PDs) versus single-photon emission computed tomography (SPECT). However, the optimal diagnostic viewing and image processing parameters for CTP are unknown.

OBJECTIVE

We sought to compare the diagnostic accuracy of different image processing techniques, cardiac phases, slice thicknesses, and viewing parameters for detection of PDs.

METHODS

A stress and rest dual-source CTP protocol was performed with adenosine. Twelve subjects with severe stenosis proven by quantitative coronary angiography (QCA), with corresponding territorial defects at SPECT, were selected as well as 7 controls (subjects with similar clinical suspicion but negative QCA and SPECT). Short-axis stress images were processed with 3 techniques: minimum intensity projection (MinIP), maximum intensity projection, and average intensity multiplanar reconstruction (MPR), 3 thicknesses (1, 3, 8 mm), and 2 phases (systolic, mid-diastolic). The resulting images (n = 1026) were randomized and interpreted by independent readers.

RESULTS

Diastolic reconstructions (8-mm MPR) showed the highest sensitivity (81%) to detect true PDs. The highest accuracy was achieved with the 8-mm (61%) and 1-mm (61%) MPR diastolic images. The most sensitive and accurate systolic reconstructions were 3-mm MinIP images. These findings related to viewing in relatively narrow window width and window level settings.

CONCLUSION

Viewing parameters for optimal accuracy in detection of perfusion defects on CTP differ for systolic and diastolic images.

Dose reduction in abdominal computed tomography: intraindividual comparison of image quality of full-dose standard and half-dose iterative reconstructions with dual-source computed tomography

OBJECTIVES

We sought to evaluate the image quality of iterative reconstruction in image space (IRIS) in half-dose (HD) datasets compared with full-dose (FD) and HD filtered back projection (FBP) reconstruction in abdominal computed tomography (CT).

MATERIALS AND METHODS

To acquire data with FD and HD simultaneously, contrast-enhanced abdominal CT was performed with a dual-source CT system, both tubes operating at 120 kV, 100 ref.mAs, and pitch 0.8. Three different image datasets were reconstructed from the raw data: Standard FD images applying FBP which served as reference, HD images applying FBP and HD images applying IRIS. For the HD data sets, only data from 1 tube detector-system was used. Quantitative image quality analysis was performed by measuring image noise in tissue and air. Qualitative image quality was evaluated according to the European Guidelines on Quality criteria for CT. Additional assessment of artifacts, lesion conspicuity, and edge sharpness was performed.

RESULTS

: Image noise in soft tissue was substantially decreased in HD-IRIS (-3.4 HU, -22%) and increased in HD-FBP (+6.2 HU, +39%) images when compared with the reference (mean noise, 15.9 HU). No significant differences between the FD-FBP and HD-IRIS images were found for the visually sharp anatomic reproduction, overall diagnostic acceptability (P = 0.923), lesion conspicuity (P = 0.592), and edge sharpness (P = 0.589), while HD-FBP was rated inferior. Streak artifacts and beam hardening was significantly more prominent in HD-FBP while HD-IRIS images exhibited a slightly different noise pattern.

CONCLUSIONS

Direct intrapatient comparison of standard FD body protocols and HD-IRIS reconstruction suggest that the latest iterative reconstruction algorithms allow for approximately 50% dose reduction without deterioration of the high image quality necessary for confident diagnosis.

Noise-resolution tradeoffs in x-ray CT imaging: a comparison of penalized alternating minimization and filtered backprojection algorithms

PURPOSE

In comparison with conventional filtered backprojection (FBP) algorithms for x-ray computed tomography (CT) image reconstruction, statistical algorithms directly incorporate the random nature of the data and do not assume CT data are linear, noiseless functions of the attenuation line integral. Thus, it has been hypothesized that statistical image reconstruction may support a more favorable tradeoff than FBP between image noise and spatial resolution in dose-limited applications. The purpose of this study is to evaluate the noise-resolution tradeoff for the alternating minimization (AM) algorithm regularized using a nonquadratic penalty function.

METHODS

Idealized monoenergetic CT projection data with Poisson noise were simulated for two phantoms with inserts of varying contrast (7%-238%) and distance from the field-of-view (FOV) center (2-6.5 cm). Images were reconstructed for the simulated projection data by the FBP algorithm and two penalty function parameter values of the penalized AM algorithm. Each algorithm was run with a range of smoothing strengths to allow quantification of the noise-resolution tradeoff curve. Image noise is quantified as the standard deviation in the water background around each contrast insert. Modulation transfer functions (MTFs) were calculated from six-parameter model fits to oversampled edge-spread functions defined by the circular contrast-insert edges as a metric of local resolution. The integral of the MTF up to 0.5 1p/mm was adopted as a single-parameter measure of local spatial resolution.

RESULTS

The penalized AM algorithm noise-resolution tradeoff curve was always more favorable than that of the FBP algorithm. While resolution and noise are found to vary as a function of distance from the FOV center differently for the two algorithms, the ratio of noises when matching the resolution metric is relatively uniform over the image. The ratio of AM-to-FBP image variances, a predictor of dose-reduction potential, was strongly dependent on the shape of the AM's nonquadratic penalty function and was also strongly influenced by the contrast of the insert for which resolution is quantified. Dose-reduction potential, reported here as the fraction (%) of FBP dose necessary for AM to reconstruct an image with comparable noise and resolution, for one penalty parameter value of the AM algorithm was found to vary from 70% to 50% for low-contrast and high-contrast structures, respectively, and from 70% to 10% for the second AM penalty parameter value. However, the second penalty, AM-700, was found to suffer from poor low-contrast resolution when matching the high-contrast resolution metric with FBP.

CONCLUSIONS

The results of this simulation study imply that penalized AM has the potential to reconstruct images with similar noise and resolution using a fraction (10%-70%) of the FBP dose. However, this dose-reduction potential depends strongly on the AM penalty parameter and the contrast magnitude of the structures of interest. In addition, the authors' results imply that the advantage of AM can be maximized by optimizing the nonquadratic penalty function to the specific imaging task of interest. Future work will extend the methods used here to quantify noise and resolution in images reconstructed from real CT data.

Reducing abdominal CT radiation dose with adaptive statistical iterative reconstruction technique

PURPOSE

To assess radiation dose reduction for abdominal computed tomography (CT) examinations with adaptive statistical iterative reconstruction (ASIR) technique.

MATERIALS AND METHODS

With institutional review board approval, retrospective review of weight adapted abdominal CT exams were performed in 156 consecutive patients with ASIR and in 66 patients with filtered back projection (FBP) on a 64-slice MDCT. Patients were categorized into 3 groups of <60 kg (n = 42), 61 to 90 kg (n = 100), and >or=91 kg (n = 80) for weight-based adjustment of automatic exposure control technique. Remaining scan parameters were held constant at 1.375:1 pitch, 120 kVp, 55 mm table feed per rotation, 5 mm section thickness. Two radiologists reviewed all CT examinations for image noise and diagnostic acceptability. CT dose index volume, and dose length product were recorded. Image noise and transverse abdominal diameter were measured in all patients. Data were analyzed using analysis of variance.

RESULTS

ASIR allowed for an overall average decrease of 25.1% in CT dose index volume compared with the FBP technique (ASIR, 11.9 +/- 3.6 mGy; FBP, 15.9 +/- 4.3 mGy) (P < 0.0001). In each of the 3 weight categories, CT examinations reconstructed with ASIR technique were associated with significantly lower radiation dose compared with FBP technique (P < 0.0001). There was also significantly less objective image noise with ASIR (6.9 +/- 2.2) than with FBP (9.5 +/- 2.0) (P < 0.0001). For the subjective analysis, all ASIR and FBP reconstructed abdominal CTs had optimal or less noise. However, 9% of FBP and 3.8% of ASIR reconstructed CT examinations were diagnostically unacceptable because of the presence of artifacts. Use of ASIR reconstruction kernel results in a blotchy pixilated appearance in 39% of CT sans which however, was mild and did not affect the diagnostic acceptability of images. The critical reproduction of visually sharp anatomic structures was preserved in all but one ASIR 40% reconstructed CT examination.

CONCLUSION

ASIR technique allows radiation dose reduction for abdominal CT examinations whereas improving image noise compared with the FBP technique.

Optimized anisotropic rotational invariant diffusion scheme on cone-beam CT

Cone-beam computed tomography (CBCT) is an important image modality for dental surgery planning, with high resolution images at a relative low radiation dose. In these scans the mandibular canal is hardly visible, this is a problem for implant surgery planning. We use anisotropic diffusion filtering to remove noise and enhance the mandibular canal in CBCT scans. For the diffusion tensor we use hybrid diffusion with a continuous switch (HDCS), suitable for filtering both tubular as planar image structures. We focus in this paper on the diffusion discretization schemes. The standard scheme shows good isotropic filtering behavior but is not rotational invariant, the diffusion scheme of Weickert is rotational invariant but suffers from checkerboard artifacts. We introduce a new scheme, in which we numerically optimize the image derivatives. This scheme is rotational invariant and shows good isotropic filtering properties on both synthetic as real CBCT data.