Analytical Reconstruction Methods Research Articles

Iterative reconstruction for limited-angle CT using implicit neural representation

Objective. Limited-angle computed tomography (CT) presents a challenge due to its ill-posed nature. In such scenarios, analytical reconstruction methods often exhibit severe artifacts. To tackle this inverse problem, several supervised deep learning-based approaches have been proposed. However, they are constrained by limitations such as generalization issue and the difficulty of acquiring a large amount of paired CT images. Approach. In this work, we propose an iterative neural reconstruction framework designed for limited-angle CT. By leveraging a coordinate-based neural representation, we formulate tomographic reconstruction as a convex optimization problem involving a deep neural network. We then employ differentiable projection layer to optimize this network by minimizing the discrepancy between the predicted and measured projection data. In addition, we introduce a prior-based weight initialization method to ensure the network starts optimization with an informed initial guess. This strategic initialization significantly improves the quality of iterative reconstruction by stabilizing the divergent behavior in ill-posed neural fields. Our method operates in a self-supervised manner, thereby eliminating the need for extensive data. Main results. The proposed method outperforms other iterative and learning-based methods. Experimental results on XCAT and Mayo Clinic datasets demonstrate the effectiveness of our approach in restoring anatomical features as well as structures. This finding was substantiated by visual inspections and quantitative evaluations using NRMSE, PSNR, and SSIM. Moreover, we conduct a comprehensive investigation into the divergent behavior of iterative neural reconstruction, thus revealing its suboptimal convergence when starting from scratch. In contrast, our method consistently produced accurate images by incorporating an initial estimate as informed initialization. Significance. This work showcases the feasibility to reconstruct high-fidelity CT images from limited-angle x-ray projections. The proposed methodology introduces a novel data-free approach to enhance medical imaging, holding promise across various clinical applications.

Hierarchical decomposed dual-domain deep learning for sparse-view CT reconstruction

Objective. X-ray computed tomography employing sparse projection views has emerged as a contemporary technique to mitigate radiation dose. However, due to the inadequate number of projection views, an analytic reconstruction method utilizing filtered backprojection results in severe streaking artifacts. Recently, deep learning (DL) strategies employing image-domain networks have demonstrated remarkable performance in eliminating the streaking artifact caused by analytic reconstruction methods with sparse projection views. Nevertheless, it is difficult to clarify the theoretical justification for applying DL to sparse view computed tomography (CT) reconstruction, and it has been understood as restoration by removing image artifacts, not reconstruction. Approach. By leveraging the theory of deep convolutional framelets (DCF) and the hierarchical decomposition of measurement, this research reveals the constraints of conventional image and projection-domain DL methodologies, subsequently, the research proposes a novel dual-domain DL framework utilizing hierarchical decomposed measurements. Specifically, the research elucidates how the performance of the projection-domain network can be enhanced through a low-rank property of DCF and a bowtie support of hierarchical decomposed measurement in the Fourier domain. Main results. This study demonstrated performance improvement of the proposed framework based on the low-rank property, resulting in superior reconstruction performance compared to conventional analytic and DL methods. Significance. By providing a theoretically justified DL approach for sparse-view CT reconstruction, this study not only offers a superior alternative to existing methods but also opens new avenues for research in medical imaging. It highlights the potential of dual-domain DL frameworks to achieve high-quality reconstructions with lower radiation doses, thereby advancing the field towards safer and more efficient diagnostic techniques. The code is available at https://github.com/hanyoseob/HDD-DL-for-SVCT.

An attenuation field network for dedicated cone beam breast CT with short scan and offset detector geometry

The feasibility of full-scan, offset-detector geometry cone-beam CT has been demonstrated for several clinical applications. For full-scan acquisition with offset-detector geometry, data redundancy from complementary views can be exploited during image reconstruction. Envisioning an upright breast CT system, we propose to acquire short-scan data in conjunction with offset-detector geometry. To tackle the resulting incomplete data, we have developed a self-supervised attenuation field network (AFN). AFN leverages the inherent redundancy of cone-beam CT data through coordinate-based representation and known imaging physics. A trained AFN can query attenuation coefficients using their respective coordinates or synthesize projection data including the missing projections. The AFN was evaluated using clinical cone-beam breast CT datasets (n = 50). While conventional analytical and iterative reconstruction methods failed to reconstruct the incomplete data, AFN reconstruction was not statistically different from the reference reconstruction obtained using full-scan, full-detector data in terms of image noise, image contrast, and the full width at half maximum of calcifications. This study indicates the feasibility of a simultaneous short-scan and offset-detector geometry for dedicated breast CT imaging. The proposed AFN technique can potentially be expanded to other cone-beam CT applications.

Machine learning for precise hit position reconstruction in Resistive Silicon Detectors

RSDs are LGAD silicon sensors with 100% fill factor, based on the principle of AC-coupled resistive read-out. Signal sharing and internal charge multiplication are the RSD key features to achieve picosecond-level time resolution and micron-level spatial resolution, thus making these sensors promising candidates as 4D-trackers for future experiments. This paper describes the use of a neural network to reconstruct the hit position of ionizing particles, an approach that can boost the performance of the RSD with respect to analytical models. The neural network has been trained in the laboratory and then validated on test beam data. The device-under-test in this work is a 450 μm-pitch matrix from the FBK RSD2 production, which achieved a resolution of about 65 μm at the DESY Test Beam Facility, a 50% improvement compared to a simple analytical reconstruction method, and a factor two better than the resolution of a standard pixel sensor of equal pitch size with binary read-out. The test beam result is compatible with the laboratory ones obtained during the neural network training, confirming the ability of the machine learning model to provide accurate predictions even in environments very different from the training one. Prospects for future improvements are also discussed.

Bilateral extended FDK: An improved weighting method for static CT imaging.

Improving imaging speed has always been the focus of research in CT technology, which is related to the radiation dose and imaging quality of moving organs, including heart and blood vessels. However, it is difficult to achieve further improvement by increasing the rotation speed of the gantry due to its structural strength limitation. Differing from the conventional CTs, the static CT employs dozens of ray sources to acquire projection data from different angular ranges, and each source only needs to be rotated in a small range to finish a full 360° scan, thus greatly increasing the scanningspeed. As sources of static CT need to be evenly distributed over 360°, the sources and detectors have to be arranged on two parallel rings independently. Such a geometry can be considered as a special case of CT systems with a significantly large cone angle, that is, a part of the detector is missing in the vicinity of the mid-plane. Due to restriction of upper and lower bounds of the cone angle of the static CT, there are uneven projection data varying in each portion of the reconstruction volume, the conventional analytical or iterative reconstruction methods may introduce artifacts in the reconstructedoutcomes. Following the weighting approach extended FDK (xFDK) by Grimmer etal., we propose an improved bilateral xFDK algorithm (bixFDK), which focuses on the reconstruction of the expanded volume. With the same philosophy as xFDK in terms of weighting function design, bixFDK takes the longitudinal offset of the detector with respect to the source into consideration, making our method applicable to a wide range of CT geometries, especially for the static CT. Based on the proposed bixFDK, a new iterative scheme bixFDK-IR is also constructed to extend the applications to a wide range of scan protocols such as sparse-viewscan. The proposed method has been validated with the simulated phantom data and the actual clinical data of the static CT, and demonstrates that it can ensure good image quality and enlarge the reconstruction volume in z-direction of the staticCT. The bixFDK algorithm is an ideal reconstruction approach for static CT geometry, and the iterative scheme of bixFDK-IR is applicable to a wide range of CT geometries and scan protocols, thus providing a wide range of applicationscenarios.

Quantitative comparison of planar coded aperture imaging reconstruction methods

Imaging distributions of radioactive sources plays a substantial role in nuclear medicine as well as in monitoring nuclear waste and its deposit. Coded Aperture Imaging (CAI) has been proposed as an alternative to parallel or pinhole collimators, but requires image reconstruction as an extra step. Multiple reconstruction methods with varying run time and computational complexity have been proposed. Yet, no quantitative comparison between the different reconstruction methods has been carried out so far.This paper focuses on a comparison based on three sets of hot-rod phantom images captured with an experimental γ-camera consisting of a Tungsten-based MURA mask with a 2 mm thick 256 × 256 pixelated CdTe semiconductor detector coupled to a Timepix© readout circuit.Analytical reconstruction methods, MURA Decoding, Wiener Filter and a convolutional Maximum Likelihood Expectation Maximization (MLEM) algorithm were compared to data-driven Convolutional Encoder-Decoder (CED) approaches. The comparison is based on the contrast-to-noise ratio as it has been previously used to assess reconstruction quality. For the given set-up, MURA Decoding, the most commonly used CAI reconstruction method, provides robust reconstructions despite the assumption of a linear model. For single image reconstruction, however, MLEM performed best of all analytical reconstruction methods, but took on average 45 times longer than MURA Decoding. The fastest reconstruction method is the Wiener Filter with a run time 4.3 times faster compared to MURA Decoding and a mediocre quality. The CED with a specifically tailored training set was able to succeed the most commonly used MURA decoding on average by a factor between 1.37 and 2.60 and an equal run time.

A streak artifact reduction algorithm in sparse-view CT using a self-supervised neural representation.

Sparse-view computed tomography (CT) has been attracting attention for its reduced radiation dose and scanning time. However, analytical image reconstruction methods suffer from streak artifacts due to insufficient projection views. Recently, various deep learning-based methods have been developed to solve this ill-posed inverse problem. Despite their promising results, they are easily overfitted to the training data, showing limited generalizability to unseen systems and patients. In this work, we propose a novel streak artifact reduction algorithm that provides a system- and patient-specificsolution. Motivated by the fact that streak artifacts are deterministic errors, we regenerate the same artifacts from a prior CT image under the same system geometry. This prior image need not be perfect but should contain patient-specific information and be consistent with full-view projection data for accurate regeneration of the artifacts. To this end, we use a coordinate-based neural representation that often causes image blur but can greatly suppress the streak artifacts while having multiview consistency. By employing techniques in neural radiance fields originally proposed for scene representations, the neural representation is optimized to the measured sparse-view projection data via self-supervised learning. Then, we subtract the regenerated artifacts from the analytically reconstructed original image to obtain the final correctedimage. To validate the proposed method, we used simulated data of extended cardiac-torso phantoms and the 2016 NIH-AAPM-Mayo Clinic Low-Dose CT Grand Challenge and experimental data of physical pediatric and head phantoms. The performance of the proposed method was compared with a total variation-based iterative reconstruction method, naive application of the neural representation, and a convolutional neural network-based method. In visual inspection, it was observed that the small anatomical features were best preserved by the proposed method. The proposed method also achieved the best scores in the visual information fidelity, modulation transfer function, and lung nodulesegmentation. The results on both simulated and experimental data suggest that the proposed method can effectively reduce the streak artifacts while preserving small anatomical structures that are easily blurred or replaced with misleading features by the existing methods. Since the proposed method does not require any additional training datasets, it would be useful in clinical practice where the large datasets cannot becollected.

Reciprocal-FDK reconstruction for x-ray diffraction computed tomography

Objective. X-ray diffraction (XRD) technology uses x-ray small-angle scattering signal for material analysis, which is highly sensitive to material inter-molecular structure. To meet the high spatial resolution requirement in applications such as medical imaging, XRD computed tomography (XRDCT) has been proposed to provide XRD intensity with improved spatial resolution from point-wise XRD scan. In XRDCT, 2D spatial tomography corresponds to a 3D reconstruction problem with the third dimension being the XRD spectrum dimension, i.e. the momentum transfer dimension. Current works in the field have studied reconstruction methods for either angular-dispersive XRDCT or energy-dispersive XRDCT for small samples. The approximations used are only suitable for regions near the XRDCT iso-center. A new XRDCT reconstruction method is needed for more general imaging applications. Approach. We derive a new FDK-type reconstruction method (Reciprocal-FDK) for XRDCT without limitation on object size. By introducing a set of reciprocal variables, the XRDCT model is transformed into a classical cone-parallel CT model, which is an extension of a circular-trajectory cone-beam CT model, after which the FDK method is applied for XRDCT reconstruction. Main results. Both analytical simulation and Monte Carlo simulation experiments are conducted to validate the XRDCT reconstruction method. The results show that when compared to existing analytical reconstruction methods, there are improvements in the proposed Reciprocal-FDK method with regard to relative structure reconstruction and XRD pattern peak reconstruction. Since cone-parallel CT does not satisfy the data completeness condition, cone-angle effect affects the reconstruction accuracy of XRDCT. The property of cone-angle effect in XRDCT is also analyzed with ablation studies. Significance. We propose a general analytical reconstruction method for XRDCT without constraint on object size. Reciprocal-FDK provides a complete derivation and theoretical support for XRDCT reconstruction by analogy to the well-studied cone-parallel CT model. In addition, the intrinsic problem with the XRDCT data model and the corresponding reconstruction error are discussed for the first time.

Reconstruction of Preclinical PET Images via Chebyshev Polynomial Approximation of the Sinogram

Over the last decades, there has been an increasing interest in dedicated preclinical imaging modalities for research in biomedicine. Especially in the case of positron emission tomography (PET), reconstructed images provide useful information of the morphology and function of an internal organ. PET data, stored as sinograms, involve the Radon transform of the image under investigation. The analytical approach to PET image reconstruction incorporates the derivative of the Hilbert transform of the sinogram. In this direction, in the present work we present a novel numerical algorithm for the inversion of the Radon transform based on Chebyshev polynomials of the first kind. By employing these polynomials, the computation of the derivative of the Hilbert transform of the sinogram is significantly simplified. Extending the mathematical setting of previous research based on Chebyshev polynomials, we are able to efficiently apply our new Chebyshev inversion scheme for the case of analytic preclinical PET image reconstruction. We evaluated our reconstruction algorithm on projection data from a small-animal image quality (IQ) simulated phantom study, in accordance with the NEMA NU 4-2008 standards protocol. In particular, we quantified our reconstructions via the image quality metrics of percentage standard deviation, recovery coefficient, and spill-over ratio. The projection data employed were acquired for three different Poisson noise levels: 100% (NL1), 50% (NL2), and 20% (NL3) of the total counts, respectively. In the uniform region of the IQ phantom, Chebyshev reconstructions were consistently improved over filtered backprojection (FBP), in terms of percentage standard deviation (up to 29% lower, depending on the noise level). For all rods, we measured the contrast-to-noise-ratio, indicating an improvement of up to 68% depending on the noise level. In order to compare our reconstruction method with FBP, at equal noise levels, plots of recovery coefficient and spill-over ratio as functions of the percentage standard deviation were generated, after smoothing the NL3 reconstructions with three different Gaussian filters. When post-smoothing was applied, Chebyshev demonstrated recovery coefficient values up to 14% and 42% higher, for rods 1–3 mm and 4–5 mm, respectively, compared to FBP, depending on the smoothing sigma values. Our results indicate that our Chebyshev-based analytic reconstruction method may provide PET reconstructions that are comparable to FBP, thus yielding a good alternative to standard analytic preclinical PET reconstruction methods.

Fundamental and Trend of Tomographic Image Reconstruction: from Analytical Reconstruction Method, through Compressed Sensing, to Deep Learning

Fundamental and Trend of Tomographic Image Reconstruction: from Analytical Reconstruction Method, through Compressed Sensing, to Deep Learning

Using the Navier-Cauchy equation for motion estimation in dynamic imaging

<p style='text-indent:20px;'>Tomographic image reconstruction is well understood if the specimen being studied is stationary during data acquisition. However, if this specimen changes its position during the measuring process, standard reconstruction techniques can lead to severe motion artefacts in the computed images. Solving a dynamic reconstruction problem therefore requires to model and incorporate suitable information on the dynamics in the reconstruction step to compensate for the motion.</p><p style='text-indent:20px;'>Many dynamic processes can be described by partial differential equations which thus could serve as additional information for the purpose of motion compensation. In this article, we consider the Navier-Cauchy equation which characterizes small elastic deformations and serves, for instance, as a simplified model for respiratory motion. Our goal is to provide a proof-of-concept that by incorporating the deformation fields provided by this PDE, one can reduce the respective motion artefacts in the reconstructed image. To this end, we solve the Navier-Cauchy equation prior to the image reconstruction step using suitable initial and boundary data. Then, the thus computed deformation fields are incorporated into an analytic dynamic reconstruction method to compute an image of the unknown interior structure. The feasibility is illustrated with numerical examples from computerized tomography.</p>

Optimization of reconstruction parameters in [18F]FDG PET brain images aiming scan time reduction

Iterative image reconstruction methods are widely used in PET due to their better image quality when compared to analytical methods. However, inaccurate quantification occurs in low activity concentration regions, which leads to biased quantification of PET images. The diagnosis of some neurodegenerative diseases, such as Alzheimer’s disease, is based on identifying such low-uptake regions. Furthermore, PET imaging in these populations should be as short as possible to limit head movements and improve patient comfort. This work aims to identify optimized reconstruction parameters of [18F]FDG PET brain images aiming to reduce image acquisition time with minimal impact on quantification. For this, [18F]FDG PET images of a Hoffman 3-D brain phantom were acquired. Analytical and iterative reconstruction methods were compared utilizing image quality and quantitative accuracy metrics. OSEM reconstruction algorithm was optimized (4 iterations and 32 subsets). It resulted in remarkably similar images compared to the current clinical settings, with a 50% reduction in scan time (5 min with a post-reconstruction filter of 4 mm). Future clinical studies are needed to confirm the results presented here.

Low-dose computed tomography reconstruction regularized by structural group sparsity joined with gradient prior

Low-dose computed tomography (LdCT) imaging can greatly reduce the radiation dose imposed to patient, however it leads to the low signal-to-noise ratio (SNR) measured projection data. Using conventional analytical reconstruction method (e.g., filtered back-projection method), the reconstruction results usually suffer from serious noise in LdCT. To obtain high-quality CT images, iterative reconstruction method combined with prior knowledge of the object is of great importance. In this work, both structural group sparsity and gradient prior sparsity are jointed as a novel regularization constraint in the proposed CT reconstruction model. To solve the optimization-based CT reconstruction problem, original problem was transformed into a series of sub-problems based on alternating direction method of multipliers framework. The merit of the proposed joint regularization method is that global and local sparsity are both utilized. To valid the performance of proposed reconstruction algorithm, we did simulated experiments with different noise levels and real data studies. The qualitative and quantitative analyses show that the proposed reconstruction algorithm has better performance than other iterative reconstruction algorithms. What's more, compared to the existing iterative reconstruction methods, the proposed reconstruction algorithm can well reconstructed important structure features and effectively suppress the noise and artifacts.

AirNet: Fused Analytical and Iterative Image Reconstruction Method With Deep Learning Regularization for High-Quality Sparse-Data On-Board CBCT

AirNet: Fused Analytical and Iterative Image Reconstruction Method With Deep Learning Regularization for High-Quality Sparse-Data On-Board CBCT

Low-dose CT with deep learning regularization via proximal forward–backward splitting

Low-dose x-ray computed tomography (LDCT) is desirable for reduced patient dose. This work develops new image reconstruction methods with deep learning (DL) regularization for LDCT. Our methods are based on the unrolling of a proximal forward–backward splitting (PFBS) framework with data-driven image regularization via deep neural networks. In contrast to PFBS-IR, which utilizes standard data fidelity updates via an iterative reconstruction (IR) method, PFBS-AIR involves preconditioned data fidelity updates that fuse the analytical reconstruction (AR) and IR methods in a synergistic way, i.e. fused analytical and iterative reconstruction (AIR). The results suggest that the DL-regularized methods (PFBS-IR and PFBS-AIR) provide better reconstruction quality compared to conventional methods (AR or IR). In addition, owing to the AIR, PFBS-AIR noticeably outperformed PFBS-IR and another DL-based postprocessing method, FBPConvNet.

AirNet: Fused analytical and iterative reconstruction with deep neural network regularization for sparse-data CT.

Sparse-data computed tomography (CT) frequently occurs, such as breast tomosynthesis, C-arm CT, on-board four-dimensional cone-beam CT (4D CBCT), and industrial CT. However, sparse-data image reconstruction remains challenging due to highly undersampled data. This work develops a data-driven image reconstruction method for sparse-data CT using deep neural networks (DNN). The new method so-called AirNet is designed to incorporate the benefits from analytical reconstruction method (AR), iterative reconstruction method (IR), and DNN. It is built upon fused analytical and iterative reconstruction (AIR) that synergizes AR and IR via the optimization framework of modified proximal forward-backward splitting (PFBS). By unrolling PFBS into IR updates of CT data fidelity and DNN regularization with residual learning, AirNet utilizes AR such as FBP during the data fidelity, introduces dense connectivity into DNN regularization, and learns PFBS coefficients and DNN parameters that minimize the loss function during the training stage; and then AirNet with trained parameters can be used for end-to-end image reconstruction. A CT atlas of 100 prostate scans was used to validate the AirNet in comparison with state-of-art DNN-based postprocessing and image reconstruction methods. The validation loss in AirNet had the fastest decreasing rate, owing to inherited fast convergence from AIR. AirNet was robust to noise in projection data and content differences between the training set and the images to be reconstructed. The impact of image quality on radiotherapy treatment planning was evaluated for both photon and proton therapy, and AirNet achieved the best treatment plan quality, especially for proton therapy. For example, with limited-angle data, the maximal target dose for AirNet was 109.5% in comparison with the ground truth 109.1%, while it was significantly elevated to 115.1% and 128.1% for FBPConvNet and LEARN, respectively. A new image reconstruction AirNet is developed for sparse-data CT image reconstruction. AirNet achieved the best image reconstruction quality both visually and quantitatively among all methods under comparison for all sparse-data scenarios (sparse-view and limited-angle), and provided the best photon and proton treatment plan quality based on sparse-data CT.

Learned Full-Sampling Reconstruction From Incomplete Data

Sparse-view and limited-angle Computed Tomography (CT) are very challenging problems in real applications. Due to the high ill-posedness, both analytical and iterative reconstruction methods may present distortions and artifacts for such incomplete data problems. In this work, we propose a novel reconstruction model to jointly reconstruct a high-quality image and its corresponding high-resolution projection data. The model is built up by deploying regularization on both CT image and projection data, as well as by introducing a novel full-sampling condition to fuse information from both domains. Inspired by the success of deep learning methods in imaging, we utilize the convolutional neural networks to embed and learn both the interrelationship between raw data and reconstructed images and prior information such as regularization, which is implemented in an end-to-end training process. Numerical results demonstrate that the proposed approach outperforms both variational and popular learning-based reconstruction methods for the sparse-view and limited-angle CT problems.

One network to solve all ROIs: Deep learning CT for any ROI using differentiated backprojection.

Computed tomography for the reconstruction of region of interest (ROI) has advantages in reducing the x-ray dose and the use of a small detector. However, standard analytic reconstruction methods such as filtered back projection (FBP) suffer from severe cupping artifacts, and existing model-based iterative reconstruction methods require extensive computations. Recently, we proposed a deep neural network to learn the cupping artifacts, but the network was not generalized well for different ROIs due to the singularities in the corrupted images. Therefore, there is an increasing demand for a neural network that works well for any ROI size. Two types of neural networks are designed. The first type learns ROI size-specific cupping artifacts from FBP images, whereas the second type network is for the inversion of the truncated Hilbert transform from the truncated differentiated backprojection (DBP) data. Their generalizabilities for different ROI sizes, pixel sizes, detector pitch and starting angles for a short scan are then investigated. Experimental results show that the new type of neural networks significantly outperform existing iterative methods for all ROI sizes despite significantly lower runtime complexity. In addition, performance improvement is consistent across different acquisition scenarios. Since the proposed method consistently surpasses existing methods, it can be used as a general CT reconstruction engine for many practical applications without compromising possible detector truncation.

Analysis of the Use of Unmatched Backward Operators in Iterative Image Reconstruction With Application to Three-Dimensional Optoacoustic Tomography

Due to their ability to model complicated imaging physics, to compensate for imperfect data acquisition systems, and to exploit prior information regarding the to-be-imaged object, iterative image reconstruction algorithms can often produce higher quality images than analytical reconstruction methods. However, for three-dimensional (3-D) imaging tasks with large fields of view, iterative reconstruction methods can be computationally burdensome. A common cause for this is the need to repeatedly evaluate the forward operator and its adjoint. From the algorithmic perspective, one way to accelerate iterative algorithms is to substitute the adjoint operator with an unmatched approximation of it, which can be computed more efficiently. Previous works have investigated some of the impacts of employing unmatched backward operators in iterative algorithms. This paper extends the theoretical analysis of unmatched backward operators to a more general penalized least-squares framework that allows for complex eigenvalues and regularization. Additionally, a convergence condition for a Landweber-type algorithm employing an unmatched backward operator is presented and numerically corroborated. An unmatched backward operator is introduced to accelerate iterative image reconstruction in 3-D optoacoustic tomography, and it is investigated by use of experimental data.

Error-Splitting Forward Model for Iterative Reconstruction in X-Ray Computed Tomography and Application With Gauss–Markov–Potts Prior

In order to enhance image quality for controlling the interior of a volume in industry, model-based iterative reconstruction (MBIR) methods in three-dimensional (3-D) X-ray computed tomography (CT) have shown their efficiency compared to analytical reconstruction methods. MBIR methods enforce a prior model on the volume to reconstruct and make fusion of the information contained in the prior model and the projection data. The projections have many uncertainties that have very different origins in 3-D CT. They are taken into account in MBIR methods but, despite of their different origins, they are in general gathered in only one term in the forward model. In this paper, we propose to derive a new forward model by adding a further error term in the Poisson statistics of photon-count, corresponding to the deviation of the monochromatic model with respect to the actual polychromacy of the rays. A Taylor expansion of the Poisson log-likelihood leads us to a new algebraic forward model accounting for two terms of uncertainties: we call it the error-splitting forward model. Different prior models are assigned to each of distinguished uncertainties: measurement uncertainties are modeled as Gaussian, while linear model uncertainties are modeled as heavy-tailed to bring robustness to the reconstruction process. We give strategies to fix the parameters of the error-splitting forward model. Next, we use it in a full MBIR method with Gauss–Markov–Potts prior model on the volume, in order to reconstruct piecewise-constant objects for non-destructive testing in industry. Compared to the conventional forward model, we show in our experiments that the use of the error-splitting forward model with Gauss–Markov–Potts prior combines better robustness and accuracy.