Adaptive Dictionary Learning in Sparse Gradient Domain for Image Recovery

Liu, Qiegen; Wang, Shanshan; Ying, Leslie; Xi, Peng; Zhu, Yanjie; Liang, Dong

doi:10.1109/tip.2013.2277798

Cited by 106 publications

(74 citation statements)

References 43 publications

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“…Then, we apply proximal algorithm [19,24] to solve the problem in (16) by incorporating the proximal mapping…”

Section: A Projected Iterative Soft-thresholding Algorithmmentioning

confidence: 99%

“…Compared to orthogonal systems, redundant systems, such as tight frames and dictionaries, can benefit from that redundancy in noise removal and artifacts reduction in signal processing [10][11][12]. Within the field of CS-MRI, the quality of reconstructed images is improved with redundant systems [6,[13][14][15][16]. For these redundant systems, there exists significant difference between these two models as reported in [8,14,17,18].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Projected Iterative Soft-Thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

Liu

Zhan

Cai

et al. 2016

IEEE Trans. Med. Imaging

163

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Abstract-Compressed sensing has shown great potentials in accelerating magnetic resonance imaging. Fast image reconstruction and high image quality are two main issues faced by this new technology. It has been shown that, redundant image representations, e.g. tight frames, can significantly improve the image quality. But how to efficiently solve the reconstruction problem with these redundant representation systems is still challenging. This paper attempts to address the problem of applying iterative soft-thresholding algorithm (ISTA) to tight frames based magnetic resonance image reconstruction. By introducing the canonical dual frame to construct the orthogonal projection operator on the range of the analysis sparsity operator, we propose a projected iterative soft-thresholding algorithm (pISTA) and further accelerate it by incorporating the strategy proposed by Beck and Teboulle in 2009. We theoretically prove that pISTA converges to the minimum of a function with a balanced tight frame sparsity. Experimental results demonstrate that the proposed algorithm achieves better reconstruction than the widely used synthesis sparse model and the accelerated pISTA converges faster or comparable to the state-of-art smoothing FISTA. One major advantage of pISTA is that only one extra parameter, the step size, is introduced and the numerical solution is stable to it in terms of image reconstruction errors, thus allowing easily setting in many fast magnetic resonance imaging applications.

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“…Then, we apply proximal algorithm [19,24] to solve the problem in (16) by incorporating the proximal mapping…”

Section: A Projected Iterative Soft-thresholding Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Projected Iterative Soft-Thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

Liu

Zhan

Cai

et al. 2016

IEEE Trans. Med. Imaging

163

View full text Add to dashboard Cite

show abstract

“…But this equation is not satisfied by many images. The natural image statistics prove that usually the areas of image primitives have very low internal dimensions and thus they can be represented by a small amount of training samples [24]. The primitives mentioned here refer to the high-frequency feature areas such as the edge and inflection points in images.…”

Section: Principle Of Sr Image Reconstructionmentioning

confidence: 99%

Hazardous Gas Emission Monitoring Based on High-Resolution Images

Chen¹,

Wang

et al. 2018

Journal of Spectroscopy

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Air pollution presents unprecedentedly severe challenges to humans today. Various measures have been taken to monitor pollution from gas emissions and the changing atmosphere, of which imaging is of crucial importance. By images of target scenes, intuitional judgments and in-depth data are achievable. However, due to the limitations of imaging devices, effective and efficient monitoring work is often hindered by low-resolution target images. To deal with this problem, a superresolution reconstruction method was proposed in this study for high-resolution monitoring images. It was based on the idea of sparse representation. Particularly, multiple dictionary pairs were trained according to the gradient features of samples, and one optimal pair of dictionaries was chosen to reconstruct by judging the weighting of the information in different directions. Furthermore, the K-means singular value decomposition algorithm was used to train the dictionaries and the orthogonal matching pursuit algorithm was employed to calculate the sparse coding coefficients. Finally, the experiment's results demonstrated its advantages in both visual fidelity and numerical measures.

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“…Therefore, some new transforms are desired to sparsely represent MR images. For example, adaptive transforms [19][20][21][22] or dictionaries [31][32][33][34][35] can improve the quality ing nor in realistic non-Cartesian sampling. Besides, there is still concern that the NUFFT or k-space re-gridding may affect the advantage of these patch-based images reconstruction.…”

Section: General Cs-mrimentioning

confidence: 99%

Patch-Based Directional Redundant Wavelets in Compressed Sensing Parallel Magnetic Resonance Imaging with Radial Sampling Trajectory

Ye¹,

Qu²,

Guo³

et al. 2016

j med imaging hlth inform

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Compressed sensing has been shown promising to speed up magnetic resonance imaging, and its combination with partially parallel imaging can further accelerate the data acquisition. For compressed sensing, a sparser representation of an image usually leads to lower reconstruction errors. Recently, a patch-based directional wavelets (PBDW), providing an adaptive sparse representation of image patches with geometric information, has been proposed in compressed sensing MRI to improve the edge reconstruction. However, it is still unknown how to incorporate PBDW into partially parallel imaging. In this work, we propose to use patch-based directional redundant wavelets (PBDRW) as an adaptive sparsifying transform in compressed sensing sensitivity encoding, and wed the new method with radial sampling to achieve higher acceleration factors. Results from simulation and in vivo data indicate that PBDRW in sensitivity encoding achieves lower reconstruction errors and preserves more image details than traditional total variation and wavelets.

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Adaptive Dictionary Learning in Sparse Gradient Domain for Image Recovery

Cited by 106 publications

References 43 publications

Projected Iterative Soft-Thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

Projected Iterative Soft-Thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

Hazardous Gas Emission Monitoring Based on High-Resolution Images

Patch-Based Directional Redundant Wavelets in Compressed Sensing Parallel Magnetic Resonance Imaging with Radial Sampling Trajectory

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