Smoothing and Decomposition for Analysis Sparse Recovery

Zhao, Tiejun; Eldar, Yonina C.; Beck, Amir; Nehorai, Arye

doi:10.1109/tsp.2014.2304932

Cited by 90 publications

(59 citation statements)

References 37 publications

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“…It can be seen that smaller leads to a more accurate reconstruction, which is consistent with [27,28]. In our method, we inherit the continuation technique of [27] to accelerate the convergence while obtaining a desired reconstruction accuracy.…”

Section: Parameters Sensitivity Analysis For Two Experiments Sce-supporting

confidence: 62%

“…To solve the weighted ℓ 1 -minimization problem (5) in the weighted reconstruction phase, an extension of the SFISTA [27] is employed. Recently, the SFISTA is a fast iterative thresholding algorithm-(FISTA-) based algorithm, which allows for solving the ℓ 1 -norm minimization problem based on analysis sparse model:…”

Section: Optimizationmentioning

confidence: 99%

“…Furthermore, the wavelet and the Contourlet are combined to sparsely represent the underlying image. In addition, to deal with the nondifferentiable terms in our model and to achieve fast convergence of the reconstruction, SFISTA [27] is extended to solve the proposed model. Experiment results indicate that the proposed algorithm improves the quality of reconstructed images in terms of both visible quality and the PSNR.…”

Section: Introductionmentioning

confidence: 99%

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Combined Similarity to Reference Image with Joint Sparsifying Transform for Longitudinal Compressive Sensing MRI

Kang

Cao

et al. 2016

Mathematical Problems in Engineering

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It is challenging to save acquisition time and reconstruct a medical magnetic resonance (MR) image with important details and features from its compressive measurements. In this paper, a novel method is proposed for longitudinal compressive sensing (LCS) MR imaging (MRI), where the similarity between reference and acquired image is combined with joint sparsifying transform. Furthermore, the joint sparsifying transform with the wavelet and the Contourlet can efficiently represent both isotropic and anisotropic features and the objective function is solved by extended smooth-based monotone version of the fast iterative shrinkage thresholding algorithm (SFISTA). The experiment results demonstrate that the existing regularization model obtains better performance with less acquisition time and recovers both edges and fine details of MR images, much better than the existing regularization model based on the similarity and the wavelet transform for LCS-MRI.

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Section: Parameters Sensitivity Analysis For Two Experiments Sce-supporting

confidence: 62%

Section: Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combined Similarity to Reference Image with Joint Sparsifying Transform for Longitudinal Compressive Sensing MRI

Kang

Cao

et al. 2016

Mathematical Problems in Engineering

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“…To solve the ℓ 1 -minimization problem (3) in the weighted reconstruction phase, we use an extension of SFISTA. 48 The extended algorithm is summarized in Algorithm II, where the notation ∥ · ∥ 2 for matrices denotes the largest singular value. The operator Γ λ µ (z) is the soft shrinkage operator, which is applied element-wise on z and is defined as (for complex A II.…”

Section: C Adaptive Weighting For Reference Based Mrimentioning

confidence: 99%

Reference‐based MRI

2016

Self Cite

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Purpose: In many clinical MRI scenarios, existing imaging information can be used to significantly shorten acquisition time or to improve Signal to Noise Ratio (SNR).In this paper the authors present a framework for fast MRI by exploiting a reference image (FASTMER).Methods: The proposed approach utilizes the possible similarity of the reference image that exists in many clinical MRI imaging scenarios. Such scenarios include similarity between adjacent slices in high resolution MRI, similarity between various contrasts in the same scan and similarity between different scans of the same patient. The authors take into account that the reference image may exhibit low similarity with the acquired image and develop an iterative weighted approach for reconstruction, which tunes the weights according to the degree of similarity.Results: Experimental results demonstrate the performance of the method in three different clinical MRI scenarios: SNR improvement in high resolution brain MRI, exploiting similarity between T2-weighted and fluid-attenuated inversion recovery (FLAIR) for fast FLAIR scanning and utilizing similarity between baseline and follow-up scans for fast follow-up. Results outperform reconstruction results of existing state-of-the-art methods. Conclusions:The authors present a method for fast MRI by exploiting a reference image. The method is based on an iterative reconstruction approach that supports cases in which similarity to the reference scan is not guaranteed, which enables the applicability of the method to a variety of MRI applications. Thanks to the existence of reference images in various clinical imaging scenarios, the proposed framework can play a major part in improving reconstruction in many MR applications.

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“…The primary computational step of STAR is the constrained minimization in line 4 of the algorithm given in Table 1. This is a convex optimization problem and can be readily solved by existing techniques (e.g., Douglas-Rachford splitting [28], ADMM [29], NESTA-UP [26], and MFISTA [30]. In addition, the positivity constraint was enforced on the estimate of F because EPR images are real-valued and positive in general.…”

Section: Theorymentioning

confidence: 99%

Accelerated dynamic EPR imaging using fast acquisition and compressive recovery

Ahmad

Samouilov

Zweíer

2016

Journal of Magnetic Resonance

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Electron paramagnetic resonance (EPR) allows quantitative imaging of tissue redox status, which provides important information about ischemic syndromes, cancer and other pathologies. For continuous wave EPR imaging, however, poor signal-to-noise ratio and low acquisition efficiency limit its ability to image dynamic processes in vivo including tissue redox, where conditions can change rapidly. Here, we present a data acquisition and processing framework that couples fast acquisition with compressive sensing-inspired image recovery to enable EPR-based redox imaging with high spatial and temporal resolutions. The fast acquisition (FA) allows collecting more, albeit noisier, projections in a given scan time. The composite regularization based processing method, called spatio-temporal adaptive recovery (STAR), not only exploits sparsity in multiple representations of the spatio-temporal image but also adaptively adjusts the regularization strength for each representation based on its inherent level of the sparsity. As a result, STAR adjusts to the disparity in the level of sparsity across multiple representations, without introducing any tuning parameter. Our simulation and phantom imaging studies indicate that a combination of fast acquisition and STAR (FASTAR) enables high-fidelity recovery of volumetric image series, with each volumetric image employing less than 10 s of scan. In addition to image fidelity, the time constants derived from FASTAR also match closely to the ground truth even when a small number of projections are used for recovery. This development will enhance the capability of EPR to study fast dynamic processes that cannot be investigated using existing EPR imaging techniques.

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Smoothing and Decomposition for Analysis Sparse Recovery

Cited by 90 publications

References 37 publications

Combined Similarity to Reference Image with Joint Sparsifying Transform for Longitudinal Compressive Sensing MRI

Combined Similarity to Reference Image with Joint Sparsifying Transform for Longitudinal Compressive Sensing MRI

Reference‐based MRI

Accelerated dynamic EPR imaging using fast acquisition and compressive recovery

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