CT Image Reconstruction from Sparse Projections Using Adaptive TpV Regularization

Dual-head small-animal positron emission tomography (DHAPET) has characteristics of high detection sensitivity and flexible system configurations. However, the system geometry may result in severe parallax errors and undetected events along the trans-axial directions, thus reducing the image quality. With the advancement of detector hardware, time-of-flight (TOF) of photons can be detected, which has demonstrated significant improvement in image quality, and can greatly benefit its use in research studies and clinics. Algorithms like total variation (TV) minimization methods that aim to compensate the effects of data truncation can be employed to reconstruct images with better resolution and quality. In this work, we will numerically compute the DHAPET system response matrix that includes TOF information and propose a TOF-PET reconstruction algorithm based on TV-minimization. By applying both TOF information and TV minimization in the iterative algorithm, the reconstructed images can be anticipated to have improved quality with better spatial resolution.

In some computed tomography (CT) applications, limited-angle projections are used for image reconstruction, and traditional reconstruction methods, such as filtered back-projection (FBP) or simultaneous algebraic reconstruction technique (SART), cannot reconstruct high-quality CT images without prior knowledge assistance. For limited-angle CT reconstruction, total variation minimization (TVM) method is not conductive to recovering image structures. Image reconstruction methods based on anisotropic total variation (ATV) and reweighted anisotropic total variation (RwATV) can significantly reduce the shading artifacts using prior knowledge of the scanning angular range and image sparsity. However, using the knowledge of image sparsity does not further improve image quality in some applications. In this paper, we propose a new reconstruction method based on anisotropic relative total variation (ARTV) for limited-angle CT reconstruction. In ARTV, the windowed inherent variation (WIV) indicates the strength of structure information and WIV values are adaptively determined by local structure information. In limited-angle CT, particular scanning angular range urges us into exerting different strengths on different directions of ARTV. Experiments on FORBILD HEAD phantom, a thoracic image and real projections of a walnut are performed to test the new method. Experimental results show that the destroyed structures are recovered to some extent, and we acquire higher image quality compared to some existing limited-angle CT reconstruction methods.

In recent years, the total variation (TV) minimization method has been widely used for compressed sensing (CS) based CT image reconstruction. In this paper, we propose a few-view reweighted sparsity hunting (FRESH) method for CT image reconstruction, and demonstrate the superior performance of this method. Specifically, the key of the purposed method is that a reweighted total variation (RwTV) measure is used to characterize image sparsity in the cost function, outperforming the conventional TV counterpart. To solve the RwTV minimization problem efficiently, the Split-Bregman method and other state-of-the-art L1 optimization methods are compared. Inspired by the fast iterative shrinkage/thresholding algorithm (FISTA), a predication step is incorporated for fast computation in the Split-Bregman framework. Extensive numerical experiments have shown that our FRESH approach performs significantly better than competing algorithms in terms of image quality and convergence speed for few-view CT. High-quality images were reconstructed by our FRESH method after 250 iterations using only 15 few-view projections of the Forbild head phantom while other competitors needed more than 800 iterations. Remarkable improvements in details in the experimental evaluation using actual sheep thorax data further indicate the potential real-world application of the FRESH method.

This work presents a novel computed tomography (CT) reconstruction method for the few-view problem based on fractional calculus. To overcome the disadvantages of the total variation minimization method, we propose a fractional-order total variation-based image reconstruction method in this paper. The presented model adopts fractional-order total variation instead of traditional total variation. Different from traditional total variation, fractional-order total variation is derived by considering more neighboring image voxels such that the corresponding weights can be adaptively determined by the model, thus suppressing the over-smoothing effect. The discretization scheme of the fractional-order model is also given. Numerical and clinical experiments demonstrate that our method achieves better performance than existing reconstruction methods, including filtered back projection (FBP), the total variation-based projections onto convex sets method (TV-POCS), and soft-threshold filtering (STH).

CT imaging plays a vital role in non-invasive diagnosis and in surgical planning of critical diseases. It is essential to reduce radiation dose during CT imaging as excessive exposure may cause harm to human tissues. To reduce radiation dose, CT image is acquired using limited number of X-ray projections and then to reconstruct the image an adaptive total generalised variation (TGV) minimisation method has been proposed. The simulation results have been compared with the existing TV, TGV and TGV with hard thresholding methods. Typically two types of noises, Gaussian and Poisson distributed noises, are introduced during CT imaging process. So, these two types of noises have been added in measured samples. It is found that after applying soft thresholding and FISTA algorithm with the proposed method, better results have been obtained in noisy imaging environment. The reconstructed CT image quality has been compared using parameters like FSSIM, PSNR, NRMSE and MAE.

The exterior computed tomography (CT) problem is one kind of truncation problem. It is very ill-posed, so that accurate reconstruction of the attenuation function is hardly possible from real data. Based on projection onto convex sets (POCS) algorithm, total variation minimization (TVM) methods, and C-V model, we develop and investigate a new iterative reconstruction algorithm, which is referred to as subregion-averaged-TVM-POCS (SA-TVM-POCS). Numerical simulations are presented to illustrate the efficiency of the algorithm. The results of this paper can be easily applied to other x-ray CT reconstruction problems.

Recent advances in compressed sensing (CS) enable accurate CT image reconstruction from highly undersampled and noisy projection measurements, due to the sparsifiable feature of most CT images using total variation (TV). These novel reconstruction methods have demonstrated advantages in clinical applications where radiation dose reduction is critical, such as onboard cone-beam CT (CBCT) imaging in radiation therapy. The image reconstruction using CS is formulated as either a constrained problem to minimize the TV objective within a small and fixed data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning, which significantly limit the clinical use of CS-based iterative reconstruction. In this paper, we propose an optimization algorithm for CS reconstruction which overcomes the above two drawbacks. The data fidelity tolerance of CS reconstruction can be well estimated based on the measured data, as most of the projection errors are from Poisson noise after effective data correction for scatter and beam-hardening effects. We therefore adopt the TV optimization framework with a data fidelity constraint. To accelerate the convergence, we first convert such a constrained optimization using a logarithmic barrier method into a form similar to that of the conventional TV regularization based reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection with an adaptive Barzilai-Borwein step-size selection scheme. The proposed algorithm is referred to as accelerated barrier optimization for CS (ABOCS), and evaluated using both digital and physical phantom studies. ABOCS directly estimates the data fidelity tolerance from the raw projection data. Therefore, as demonstrated in both digital Shepp-Logan and physical head phantom studies, consistent reconstruction performances are achieved using the same algorithm parameters on scans with different noise levels and∕or on different objects. On the contrary, the penalty weight in a TV regularization based method needs to be fine-tuned in a large range (up to seven times) to maintain the reconstructed image quality. The improvement of ABOCS on computational efficiency is demonstrated in the comparisons with adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS), an existing CS reconstruction algorithm also using constrained optimization. ASD-POCS alternatively minimizes the TV objective using adaptive steepest descent (ASD) and the data fidelity error using projection onto convex sets (POCS). For similar image qualities of the Shepp-Logan phantom, ABOCS requires less computation time than ASD-POCS in MATLAB by more than one order of magnitude. We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter settings for different datasets. These advantages have been demonstrated on phantom studies.

Isotropic and anisotropic filtering norm-minimization: A generalization of the TV and TGV minimizations using NESTA

In practical applications of tomographic imaging, there are often challenges for image reconstruction due to under-sampling and insufficient data. In computed tomography (CT), for example, image reconstruction from few views would enable rapid scanning with a reduced x-ray dose delivered to the patient. Limited-angle problems are also of practical significance in CT. In this work, we develop and investigate an iterative image reconstruction algorithm based on the minimization of the image total variation (TV) that applies to divergent-beam CT. Numerical demonstrations of our TV algorithm are performed with various insufficient data problems in fan-beam CT. The TV algorithm can be generalized to cone-beam CT as well as other tomographic imaging modalities.

The quantitative analysis of the blood flow in the brain tissue is one of the important problems in neurosurgery. It arises when diagnosing acute ischemic stroke. This problem can be solved using computed tomography (CT) perfusion imaging. There are various methods for extracting quantitative characteristics of cerebral blood flow from CT perfusion data, which differ in degrees of their noise resistance. More noise-resistant methods enable the reduction in radiation doses when conducting the examination of the patient. Hence, the development of noise-resistant methods is an important problem. This paper presents an algorithm for evaluating the quantitative characteristics of cerebral blood flow, based on the regularization using the projection onto a set of monotonic functions while minimizing the functional of total generalized variation (TGV). The proposed approach is tested on synthetic and real-world data. It yields better results than the singular value decomposition (SVD) method with Tikhonov regularization and methods of total variation (TV) minimization and TGV minimization.

ABSTRACTLimited data CT Image reconstruction is a real-life problem. A Total Variation (TV) l1 norm minimization technique has been examined and validated here to reconstruct CT images from limited data incorporating a limited number of views along with limited angular span, a situation typical in engineering applications. The Lagrangian technique has been used to solve TV equations. The reconstructed CT image has been compared with the images reconstructed by SIRT, Higher Order TV (HOTV) technique, l2 norm minimization based technique and some other techniques with the help of various image quality index (IQI) parameters. The comparison shows that the proposed scheme is an attractive solution for limited data CT Image reconstruction from industrial and engineering perspective. The application of Sobolev space error analysis has also been given to ensure good global reconstruction.

The total variation (TV) minimization image reconstruction algorithm for inverting the divergent-beam x-ray transform is applied to image reconstruction in circular cone-beam computed tomography (CT). Reconstructions for the disk phantom are shown and compared with that of projection onto convex sets (POCS). The preliminary results appear to show that TV-minimization yields accurate image reconstructions that are robust against data inconsistencies due to noise or mismatch in the system matrix.

A computational and experimental study is conducted to examine how directivity associated with a finite aperture sensor affects photoacoustic tomography (PAT) image reconstruction. Acoustic signals for the simulation work were computed using a discrete particle approach from three numerical phantoms including a vasculature. The theoretical framework and a Monte Carlo approach for construction of a tissue configuration are discussed in detail. While simulating forward data, the directivity of the sensor was taken into account. The image reconstruction was accomplished using system matrix based methods like l2 norm Tikhonov regularization, l1 norm regularization and total variation (TV) minimization. Accordingly, two different system matrices were constructed- (i) assuming transducer as a point detector (PD) and (ii) retaining properties of a finite detector with directivity (FDWD). Image reconstruction was also performed utilizing experimentally measured PA signals. Both the computational and experimental results demonstrate that blur-free PAT imaging can be achieved with the FDWD method. Additionally, TV minimization provides marginally better image reconstruction compared to the other schemes.

X-ray Computed Tomography (CT) scans, while useful, emit harmful radiation which is why low-dose image acquisition is desired. However, noise corruption in these cases is a difficult obstacle. CT image denoising is a challenging topic because of the difficulty in modeling noise. In this study, we propose taking an image decomposition approach to removing noise from low-dose CT images. We model the image as the superposition of a structure layer and a noise layer. Total Variation (TV) minimization is used to learn two dictionaries to represent each layer independently, and sparse coding is used to separate them. Finally, an iterative post-processing stage is introduced that uses image-adapted curvelet dictionaries to recover blurred edges. Our results demonstrate that image separation is a viable alternative to the classic K-SVD denoising method.

To reduce the cost of positron emission tomography (PET) scanning systems, image reconstruction algorithms for low-sampled data have been extensively studied. However, the current method based on total variation (TV) minimization regularization nested in the maximum likelihood-expectation maximization (MLEM) algorithm cannot distinguish true structures from noise resulting losing some fine features in the images. Thus, this work aims to recover fine features lost in the MLEM-TV algorithm from low-sampled data. A feature refinement (FR) approach previously developed for statistical interior computed tomography (CT) reconstruction is applied to PET imaging to recover fine features in this study. The proposed method starts with a constant initial image and the FR step is performed after each MLEM-TV iteration to extract the desired structural information lost during TV minimization. A feature descriptor is specifically designed to distinguish structure from noise and artifacts. A modified steepest descent method is adopted to minimize the objective function. After evaluating the impacts of different patch sizes on the outcome of the presented method, an optimal patch size of 7×7 is selected in this study to balance structure-detection ability and computational efficiency. Applying MLEM-TV-FR algorithm to the simulated brain PET imaging using an emission activity phantom, a standard Shepp-Logan phantom, and mouse results in the increased peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as comparing to using the conventional MLEM-TV algorithm, as well as the substantial reduction of the used sampling numbers, which improves the computational efficiency. The presented algorithm can achieve image quality superior to that of the MLEM and MLEM-TV approaches in terms of the preservation of fine structure and the suppression of undesired artifacts and noise, indicating its useful potential for low-sampled data in PET imaging.