Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data

Wang, Cheng-Xiang; Zeng, Li; Guo, Yumeng; Zhang, Lingli

doi:10.3934/ipi.2017043

Cited by 20 publications

(8 citation statements)

References 44 publications

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“…Other attempts at sparsity promoting variational models for limited-angle tomography rely on dictionary learning [80] or use a regulariser that promotes sparse solutions with respect to wavelets [90,94] or curvelets/shearlets [30,71]. One can further constrain a sparse solution against a given prior image as shown in [18,90,94,34].…”

Section: Variational Models For Reconstructionmentioning

confidence: 99%

Deep Microlocal Reconstruction for Limited-Angle Tomography

Andrade-Loarca¹,

Kutyniok²,

Öktem³

et al. 2021

Preprint

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We present a deep learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a recently developed digital wavefront set extractor as well as the well-known microlocal canonical relation for the Radon transform. We use the wavefront set information about x-ray data to improve the reconstruction by requiring that the underlying neural networks simultaneously extract the correct ground truth wavefront set and ground truth image. As a necessary theoretical step, we identify the digital microlocal canonical relations for deep convolutional residual neural networks. We find strong numerical evidence for the effectiveness of this approach.

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Section: Variational Models For Reconstructionmentioning

confidence: 99%

Deep Microlocal Reconstruction for Limited-Angle Tomography

Andrade-Loarca¹,

Kutyniok²,

Öktem³

et al. 2021

Preprint

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“…However, the edges of the reconstructed images may still suffer from a certain degree of distortion. To better preserve the edges and suppress the artifacts, the image gradient

L_{0}

norm has been extensively utilized as regularizers for limited‐angle reconstruction 45,48,50 . By means of the stronger edge‐preserving ability of the

L_{0}

norm, these methods recover edge structure information more effectively.…”

Section: Introductionmentioning

confidence: 99%

“…To better preserve the edges and suppress the artifacts, the image gradient L 0 norm has been extensively utilized as regularizers for limited-angle reconstruction. 45,48,50 By means of the stronger edge-preserving ability of the L 0 norm, these methods recover edge structure information more effectively. Especially, AEDS algorithm was proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

A neural network with encoded visible edge prior for limited‐angle computed tomography reconstruction

Zhang

Zhao

et al. 2021

Medical Physics

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Purpose Limited‐angle computed tomography is a challenging but important task in certain medical and industrial applications for nondestructive testing. The limited‐angle reconstruction problem is highly ill‐posed and conventional reconstruction algorithms would introduce heavy artifacts. Various models and methods have been proposed to improve the quality of reconstructions by introducing different priors regarding to the projection data or ideal images. However, the assumed priors might not be practically applicable to all limited‐angle reconstruction problems. Convolutional neural network (CNN) exhibits great promise in the modeling of data coupling and has recently become an important technique in medical imaging applications. Although existing CNN methods have demonstrated promising results, their robustness is still a concern. In this paper, in light of the theory of visible and invisible boundaries, we propose an alternating edge‐preserving diffusion and smoothing neural network (AEDSNN) for limited‐angle reconstruction that builds the visible boundaries as priors into its structure. The proposed method generalizes the alternating edge‐preserving diffusion and smoothing (AEDS) method for limited‐angle reconstruction developed in the literature by replacing its regularization terms by CNNs, by which the piecewise constant assumption assumed by AEDS is effectively relaxed. Methods The AEDSNN is derived by unrolling the AEDS algorithm. AEDSNN consists of several blocks, and each block corresponds to one iteration of the AEDS algorithm. In each iteration of the AEDS algorithm, three subproblems are sequentially solved. So, each block of AEDSNN possesses three main layers: data matching layer, x‐direction regularization layer for visible edges diffusion, and y‐direction regularization layer for artifacts suppressing. The data matching layer is implemented by conventional ordered‐subset simultaneous algebraic reconstruction technique (OS‐SART) reconstruction algorithm, while the two regularization layers are modeled by CNNs for more intelligent and better encoding of priors regarding to the reconstructed images. To further strength the visible edge prior, the attention mechanism and the pooling layers are incorporated into AEDSNN to facilitate the procedure of edge‐preserving diffusion from visible edges. Results We have evaluated the performance of AEDSNN by comparing it with popular algorithms for limited‐angle reconstruction. Experiments on the medical dataset show that the proposed AEDSNN effectively breaks through the piecewise constant assumption usually assumed by conventional reconstruction algorithms, and works much better for piecewise smooth images with nonsharp edges. Experiments on the printed circuit board (PCB) dataset show that AEDSNN can better encode and utilize the visible edge prior, and its reconstructions are consistently better compared to the competing algorithms. Conclusions A deep‐learning approach for limited‐angle reconstruction is proposed in this paper, which significantly ...

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“…In recent years, researchers are becoming increasingly interested in regularized iterative reconstruction algorithms for incomplete projection data, as these algorithms can add some prior knowledge to obtain better reconstructed image and will not be affected by the geometrical structure of the scanning mode. Hence, more and more researchers are keen to construct an appropriate transformation that can utilize prior information of the reconstructed object, and various regularized iterative reconstruction algorithms have been proposed [6][7][8][9][10]. As one of the regularized iterative reconstruction algorithms, total variation (TV)-based minimization method [11] can suppress the streak artifacts and noise when the projection data are acquired within a few-views scanning mode.…”

Section: Introductionmentioning

confidence: 99%

Deep learning based image reconstruction algorithm for limited-angle translational computed tomography

et al. 2020

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As a low-end computed tomography (CT) system, translational CT (TCT) is in urgent demand in developing countries. Under some circumstances, in order to reduce the scan time, decrease the X-ray radiation or scan long objects, furthermore, to avoid the inconsistency of the detector for the large angle scanning, we use the limited-angle TCT scanning mode to scan an object within a limited angular range. However, this scanning mode introduces some additional noise and limited-angle artifacts that seriously degrade the imaging quality and affect the diagnosis accuracy. To reconstruct a high-quality image for the limited-angle TCT scanning mode, we develop a limited-angle TCT image reconstruction algorithm based on a U-net convolutional neural network (CNN). First, we use the SART method to the limited-angle TCT projection data, then we import the image reconstructed by SART method to a well-trained CNN which can suppress the artifacts and preserve the structures to obtain a better reconstructed image. Some simulation experiments are implemented to demonstrate the performance of the developed algorithm for the limited-angle TCT scanning mode. Compared with some state-of-the-art methods, the developed algorithm can effectively suppress the noise and the limited-angle artifacts while preserving the image structures. OPEN ACCESS Citation: Wang J, Liang J, Cheng J, Guo Y, Zeng L (2020) Deep learning based image reconstruction algorithm for limited-angle translational computed tomography. PLoS ONE 15(1): e0226963. https://

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Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data

Cited by 20 publications

References 44 publications

Deep Microlocal Reconstruction for Limited-Angle Tomography

Deep Microlocal Reconstruction for Limited-Angle Tomography

A neural network with encoded visible edge prior for limited‐angle computed tomography reconstruction

Deep learning based image reconstruction algorithm for limited-angle translational computed tomography

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