Improved Simultaneous Algebraic Reconstruction Technique Algorithm for Positron-Emission Tomography Image Reconstruction via Minimizing the Fast Total Variation

Boudjelal, Abdelwahhab; Messali, Zoubeida; Elmoataz, Abderrahim; Attallah, Bilal

doi:10.1016/j.jmir.2017.09.005

Cited by 11 publications

(9 citation statements)

References 43 publications

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“…For example, total variance minimization (TVM) combines iterative reconstruction and regularization of total variance to recover the lost information and reduces the artifacts introduced by the missing wedge. [ 21,22 ] This method is inspired by compressive sensing, [ 23,24 ] and it essentially deploys the sparsity constraint in the gradient domain of the tomogram. Some caveats of TVM are that it is not parameter‐free and is also computationally expensive.…”

Section: Figurementioning

confidence: 99%

“…Therefore, to constrain the solution space, strong priors need to be used to regularize the problem. For example, total variance minimization (TVM) combines iterative reconstruction and regularization of total variance to recover the lost information and reduced the artifacts introduced by the missing wedge [14,15]. This method is inspired by compressive sensing [16,17] and it essentially deploys the sparsity constraint in the gradient domain of the tomogram.…”

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confidence: 99%

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0.7 Å Resolution Electron Tomography Enabled by Deep‐Learning‐Aided Information Recovery

Wang

Ding

Liu

et al. 2020

Advanced Intelligent Systems

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As the architectural complexity of integrated circuits and functional nanomaterials advances into the atomic-scale regimes, high-resolution transmission electron microscopy (TEM) has become an essential tool in validating the structure of nanomaterials and devices. In contrast to conventional TEM imaging, which only provides projected 2D information, electron tomography is a powerful tool that can probe the 3D internal structure and chemistry of materials at the nanoscale and the atomic scale. [1] Due to its high resolution, it has been widely used in biological, [2,3] physical, [4,5] and materials science [6-10] applications. Recently, with the development of discrete tomography [11-13] and atomic-scale electron tomography, [14-18] deciphering the structure of materials atom by atom has become possible. Electron tomography renders 3D reconstruction of an object by taking a series of 2D projections from a wide range of orientations. Ideally, projection images from À90 to þ90 around a fixed axis are needed to render a perfect 3D reconstruction. [19] However, due to the limited space in an electron microscope or shadowing from the holder/sample/ support, it is hard to obtain projections for the full tilt range in many conditions. With a specialized tomography holder, images from À70 to þ70 can be obtained in most TEMs, whereas in liquid-cell tomography, the tilt range is very limited to typically <30 , because the liquid flow holders are much bulkier. [20] The limited tilt range unavoidably leads to a "missing wedge" of information, which renders artifacts in the reconstructed tomograms. These artifacts introduced by the missing wedge reduce the resolution and reliability of the reconstructed tomograms and, sometimes, can even lead to serious misinterpretations. [6] So far, the missing-wedge problem has been the main source of systematic error that limits the application of electron tomography. Mathematically speaking, when there are insufficient number of projections, the inverse problem of tomography is ill-posed, because the solution is non-unique. Therefore, to constrain the solution space, strong priors need to be used to regularize the problem. For example, total variance minimization (TVM) combines iterative reconstruction and regularization of total variance to recover the lost information and reduces the artifacts introduced by the missing wedge. [21,22] This method is inspired by compressive sensing, [23,24] and it essentially deploys the sparsity constraint in the gradient domain of the tomogram. Some caveats of TVM are that it is not parameter-free and is also computationally expensive. Keeping these aside, the real problem of TVM or any generalized TVM approach is that they are bound to one regularization that promotes one prior constraint on the solution, which may or may not be suitable for the object of interest. For example, TVM promotes piecewise constants, rendering cartoon-like tomograms lacking gradient details.

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Section: Figurementioning

confidence: 99%

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confidence: 99%

0.7 Å Resolution Electron Tomography Enabled by Deep‐Learning‐Aided Information Recovery

Wang

Ding

Liu

et al. 2020

Advanced Intelligent Systems

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“…Based on the above understanding of past works [20][21][22][23][24], this paper proposes a novel scheme based on iterative filtering for computing the MLEM algorithm for ECT image reconstruction from noisy projections, namely a filtered MLEM. More precisely, we include an additional Beltrami [25][26][27] filtering step at each iteration of the MLEM to reduce noise and unwanted artifacts while preserving the edge information.…”

Section: Introductionmentioning

confidence: 99%

A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images

et al. 2021

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The implementation of emission-computed tomography (ECT), including positron emission tomography and single-photon emission-computed tomography, has been an important research topic in recent years and is of significant and practical importance. However, the slow rate of convergence and the computational complexity have severely impeded the efficient implementation of iterative reconstruction. By combining the maximum-likelihood expectation maximization (MLEM) iteratively along with the Beltrami filter, this paper proposes a new approach to reformulate the MLEM algorithm. Beltrami filtering is applied to an image obtained using the MLEM algorithm for each iteration. The role of Beltrami filtering is to remove mainly out-of-focus slice blurs, which are artifacts present in most existing images. To improve the quality of an image reconstructed using MLEM, the Beltrami filter employs similar structures, which in turn reduce the number of errors in the reconstructed image. Numerical image reconstruction tomography experiments have demonstrated the performance capability of the proposed algorithm in terms of an increase in signal-to-noise ratio (SNR) and the recovery of fine details that can be hidden in the data. The SNR and visual inspections of the reconstructed images are significantly improved compared to those of a standard MLEM. We conclude that the proposed algorithm provides an edge-preserving image reconstruction and substantially suppress noise and edge artifacts.

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“…The regularization techniques are generally divided into a projection method and a penalty method [15]. In this paper, we use the penalty method techniques which are the Tikhonov regularization [16,17], TV method [18,19] (Fig. 4).…”

Section: Introductionmentioning

confidence: 99%

A New Method of Image Reconstruction for PET Using a Combined Regularization Algorithm

Boudjelal

Moataz

Messali

2020

Lecture Notes in Computer Science

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Positron emission tomography (PET), is a medical imaging technique that provides functional information about physiological processes. The goal of PET is to reconstruct the distribution of the radioisotopes in the body by measuring the emitted photons. The computer methods are designed to solve the inverse problem known as "image reconstruction from projections." In this paper, an iterative image reconstruction algorithm ART was regularized by combining Tikhonov and total variation regularizations. In the first step, combined regularization algorithm of total variation and Tikhonov regularization was applied to the image obtained by ART algorithm in each iteration for background noise removal with preserving edges. The quality measurements and visual inspections show a significant improvement in image quality compared to other algorithms.

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Improved Simultaneous Algebraic Reconstruction Technique Algorithm for Positron-Emission Tomography Image Reconstruction via Minimizing the Fast Total Variation

Cited by 11 publications

References 43 publications

0.7 Å Resolution Electron Tomography Enabled by Deep‐Learning‐Aided Information Recovery

0.7 Å Resolution Electron Tomography Enabled by Deep‐Learning‐Aided Information Recovery

A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images

A New Method of Image Reconstruction for PET Using a Combined Regularization Algorithm

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