Wavelet Tree Support Detection for Compressed Sensing MRI Reconstruction

Deka, Bhabesh; Datta, Sumit; Handique, Sanjeev

doi:10.1109/lsp.2018.2824251

Cited by 18 publications

(7 citation statements)

References 27 publications

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“…Incorporating the structure information of the unknown into classical optimization methods is of good potential. The parent-child dependency of wavelet coefficients can be modeled by Hidden Markov Tree (HMT) by constructing state transition matrices, which describe the probability that a wavelet coefficient is large or small when its parent is large or small [55]. Also, the hierarchical structure of wavelet coefficients can be combined within the Bayesian inference framework [56].…”

Section: Discussionmentioning

confidence: 99%

Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

Zhang

Lambert

Fraysse

et al. 2022

IEEE Open J. Antennas Propag.

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A group sparsity penalized CSI in the wavelet domain is proposed to alleviate ill-posedness within the framework of a contrast-source inversion (CSI) method. It is then applied to the retrieval of a large inhomogeneous dielectric scatterer from time-harmonic single-frequency data. As dependency exists between wavelet coefficients at different scales, referred to as the parent-child relationship, it enables to yield the wavelet quad tree structure. Therefore, wavelet coefficients can be regarded not only as pixel-wise sparse, but also group-wise sparse. Focus is put on using the dual-tree complex wavelet transform (CWT) to properly achieve the sought-after group-wise sparse representation of the spatial distribution of the contrast. It provides a 2,1 norm which is added to the standard cost functional to enforce group sparsity onto the wavelet coefficients of the spatially-varying contrast. The replication strategy is combined with the proximal method in order to solve the overlapping group penalized problem. Simulations from synthetic data in different configurations with in particular different signal-to-noise ratios illustrate pros and cons of the proposed method. The approach is shown to overcome the standard CSI method in demanding situations. Comparisons with the discrete wavelet transform (DWT) as usually performed and the 1 norm confirm the advantage of the proposed methodology.

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Section: Discussionmentioning

confidence: 99%

Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

Zhang

Lambert

Fraysse

et al. 2022

IEEE Open J. Antennas Propag.

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“…Two of the most common transforms used in CS and RPCA to promote sparsity are wavelets [28][29][30][31][32][33] and temporal Fourier [34]. Wavelets project a signal of finite energy on a frequency subband.…”

Section: Sparsifying Transformsmentioning

confidence: 99%

Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data

et al. 2022

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The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by L+S. The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. L+S decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a L+S decomposition for undersampled MR data.

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“…As shown in Figure 11, the block textures of the high-frequency image are much lower than the overall image when the sub-block size is 32 × 32, so the subblock textures are more balanced after the high-frequency image blocks are sorted. When the differences between the recon-FIGURE 12 The textures complexity comparison of the first 260 column vectors in 32 × 32 sub-block struction effects of the sub-block reconstruction are smaller, the blocking artefacts become less obvious. From the comparison of the textures of first 260 column vectors in Figure 12, the differences among the column vectors and the 256 blocks after the first iteration of the BCS-RMP method are better reflected.…”

Section: The Reconstruction Performance With Different Block Sizesmentioning

confidence: 99%

Blocking artefacts reduction based on a ripple matrix permutation image of high‐frequency images in the wavelet domain

Liu

Zhang

et al. 2021

IET Image Processing

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Block compressed sensing (BCS) approaches based on matrix permutations effectively reduce blocking artefacts in the high-quality reconstruction of images. To further reduce the blocking artefacts, the paper proposes a novel method for their processing in the wavelet domain based on the ripple matrix permutation (RMP) BCS approach. The method makes use of the energy distribution characteristics of images in the wavelet domain. The low-frequency images contain the basic information. The high-frequency images contain the edge textures information of the image, and these images are extremely sparse. Then, the proposed method performs matrix permutations only on the high-frequency images. This avoids the obvious energy differences among the blocks. The method can better balance the textures among blocks; in turn, the blocking artefacts are reduced. The approach involves performing a wavelet decomposition on the image. Then, the transformed high-frequency image is subjected to a RMP to achieve textures balancing. Finally, compressed sensing processing is performed on the permuted high-frequency image. As a result, the balancing effect becomes more significant, and the low-frequency part of the image remains unchanged, the differences among the blocks are reduced. Simulation results demonstrate that the high-frequency part of the image wavelet domain is texture balanced. When the image is reconstructed after the compressed sensing step, the image quality is significantly improved.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Wavelet Tree Support Detection for Compressed Sensing MRI Reconstruction

Cited by 18 publications

References 27 publications

Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data

Blocking artefacts reduction based on a ripple matrix permutation image of high‐frequency images in the wavelet domain

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