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

Liu, Yunsong; Zhan, Zhifang; Cai, Jian-Feng; Guo, Di; Chen, Zhong; Qu, Xiaobo

doi:10.1109/tmi.2016.2550080

Cited by 156 publications

(113 citation statements)

References 54 publications

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“…The first two columns: radial sampling with rate 10%; the last two columns: Cartesian sampling with rate 20%. From top to bottom, the full sampled phantom image (or sampling mask), reconstructed images (or reconstruction error) using DLMRI, pFISTA,, FDLCP, and the proposed method. [Color figure can be viewed at wileyonlinelibrary.com]…”

Section: Resultsmentioning

confidence: 99%

“…The proposed method is compared with three state‐of‐the‐art methods: the DLMRI method, which is a classical dictionary learning method; the FDLCP method, which learns multiclass dictionaries for MR images according to the geometrical direction of patches; and the pFISTA method, which exploits the sparsity of MR images under tight frames with a balanced model . As for all other methods, the zero‐filling image,

x^{0} = F_{u}^{T} y

, is used as the initial numerical solution.…”

Section: Methodsmentioning

confidence: 99%

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A cosparse analysis model with combined redundant systems for MRI reconstruction

Luo¹,

Ling²,

Gong³

et al. 2019

Medical Physics

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Purpose Magnetic resonance imaging (MRI) is widely used due to its noninvasive and nonionizing properties. However, MRI requires a long scanning time. In this paper, our goal is to reconstruct a high‐quality MR image from its sampled k‐space data to accelerate the data acquisition in MRI. Methods We propose a cosparse analysis model with combined redundant systems to fully exploit the sparsity of MR images. Two fixed redundant systems are used to characterize different structures, namely, the wavelet tight frame and Gabor frame. An alternating iteration scheme is used for reconstruction with simple implementation and good performance. Results The proposed method is tested on two MR images under three sampling patterns with sampling ratios ranging from 10% to 60%. The results show that the proposed method outperforms other state‐of‐the‐art MRI reconstruction methods in terms of both subjective visual quality and objective quantitative measurement. For instance, for brain images under random sampling with a ratio of 10%, compared to the other three methods, the proposed method improves the peak signal‐to‐noise ratio (PSNR) by more than 9 dB. Conclusions To better characterize different sparsities of different structures of MRI, a cosparse analysis model combining the wavelet tight frame and Gabor frame is proposed. A partial ℓ2 norm regularization is leveraged to obtain the optimal solution in a lower dimension. Compared to other state‐of‐the‐art MRI reconstruction methods, the proposed method improves the reconstruction quality of MRI, especially highly undersampled MRI.

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Section: Resultsmentioning

confidence: 99%

x^{0} = F_{u}^{T} y

, is used as the initial numerical solution.…”

Section: Methodsmentioning

confidence: 99%

A cosparse analysis model with combined redundant systems for MRI reconstruction

Luo¹,

Ling²,

Gong³

et al. 2019

Medical Physics

View full text Add to dashboard Cite

show abstract

“…Other sparsity models include generalized analysis models [24], and the balanced sparse model for tight frames [61], where the signal is sparse in a synthesis dictionary and also approximately sparse in the corresponding transform (transpose of the dictionary) domain, with a common sparse representation in both domains. These models have been applied to inverse problems such as in compressed sensing MRI [15], [61], [62]. The drawback of all of the models discussed in this section is that, traditionally, the underlying operators such as T and D are designed mathematically, typically with empirical validation on real data, rather than being computed directly from training data or adapted to a specific patient's data.…”

Section: Sparsity Using Mathematical Modelsmentioning

confidence: 99%

Image Reconstruction: From Sparsity to Data-Adaptive Methods and Machine Learning

2020

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The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or lowrank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

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“…However, fixed bases fail to sparsely represent complicated MR images with underlying image edges and textures. To address this issue, several dictionary learning models (DLMRI [4], BPFA [5] and FDLCP [6]) and different wavelet regularizations based on geometric information (PBDW [7] and PBDW with pFISTA [8]) are exploited. For instance, a fast orthogonal dictionary learning method (FDLCP) is introduced to provide adaptive sparse representation of images, in which image is divided into classified patches according to the same geometrical direction and dictionary is trained within each class for enhanced sparsity.…”

Section: Introductionmentioning

confidence: 99%

Compressed sensing MRI via a multi-scale dilated residual convolution network

Dai

Zhuang

2019

Magnetic Resonance Imaging

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Magnetic resonance imaging (MRI) reconstruction is an active inverse problem which can be addressed by conventional compressed sensing (CS) MRI algorithms that exploit the sparse nature of MRI in an iterative optimization-based manner. However, two main drawbacks of iterative optimization-based CSMRI methods are time-consuming and are limited in model capacity. Meanwhile, one main challenge for recent deep learning-based CSMRI is the trade-off between model performance and network size. To address the above issues, we develop a new multi-scale dilated network for MRI reconstruction with high speed and outstanding performance. Comparing to convolutional kernels with same receptive fields, dilated convolutions reduce network parameters with smaller kernels and expand receptive fields of kernels to obtain almost same information. To maintain the abundance of features, we present global and local residual learnings to extract more image edges and details. Then we utilize concatenation layers to fuse multi-scale features and residual learnings for better reconstruction. Compared with several non-deep and deep learning CSMRI algorithms, the proposed method yields better reconstruction accuracy and noticeable visual improvements. In addition, we perform the noisy setting to verify the model stability, and then extend the proposed model on a MRI super-resolution task.Multi-scale.The first category of CSMRI algorithms are iterative optimization-based CSMRI, in which the sparsity is enforced in specific transform domain or underlying latent representation of images, and then an alternating iterative optimization scheme is adopted to CSMRI reconstruction [2]- [11]. A pioneering work of CSMRI is Sparse MRI [2], which exploits an off-the-shelf basis to capture a specific feature (wavelets recover point-like features, contourlets capture curvelike features). A hybrid TV regularizer combined with a L 0 -regularized treestructured sparsity constraint [3] is introduced to overcome model-dependent difference 0.69/0.003 3.21/0.032 0.49/0.011 and Fig. 13. It is noted that the proposed MDN performs better reconstruction results than VDSR on a huge dataset. CONCLUSION AND PROSPECTA novel multi-scale dilated network (MDN) has been presented for CSMRI. The proposed MDN is composed by cascading two basic blocks where dilated convolutions, global and local residual learnings, and concatenation layers are integrated to extend the receptive fields of convolutional kernels for reducing network parameters, maintaining features abundance, and fusing multi-scale features, respectively. Final experiments demonstrate that MDN achieves outstanding performance with training huge and diverse data, and the proposed network outperforms several competitive CSMRI algorithms in subjective and objective assessments. In addition, the proposed model is effective in MR noisy

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

Cited by 156 publications

References 54 publications

A cosparse analysis model with combined redundant systems for MRI reconstruction

A cosparse analysis model with combined redundant systems for MRI reconstruction

Image Reconstruction: From Sparsity to Data-Adaptive Methods and Machine Learning

Compressed sensing MRI via a multi-scale dilated residual convolution network

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