On Collaborative Compressive Sensing Systems: The Framework, Design, and Algorithm

Zhu, Zhihui; Li, Gang; Ding, Jiajun; Li, Qiuwei; He, Xiongxiong

doi:10.1137/17m1148426

Cited by 15 publications

(9 citation statements)

References 60 publications

(257 reference statements)

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“…Towards that end, it is important to develop a quantized (even 1-bit) sparse sensing matrix. We finally note that it remains an open problem to certify certain properties (such as the RIP) for the optimized sensing matrices [9][10][11][12][13][14][15][16][17][18][19], which empirically outperforms a random one that satisfies the RIP. Works in these directions are ongoing.…”

Section: Lenamentioning

confidence: 99%

“…Although random matrices satisfy the RIP with high probability [7], confirming whether a general matrix satisfies the RIP is NP-hard [8]. Alternatively, mutual coherence, another measure of sensing matrices that is much easier to verify, has been introduced in practice to quantify and design sensing matrices [9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Optimized structured sparse sensing matrices for compressive sensing

et al. 2019

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We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few nonzero entries per row and a dense base matrix for capturing signals efficiently. We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence. Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests. An alternating minimization algorithm with global sequence convergence is proposed for solving the corresponding optimization problem. Numerical experiments on synthetic data and natural images show that the obtained structured sensing matrix results in a higher signal reconstruction than a random dense sensing matrix. (Zhihui Zhu), qiuli@mines.edu (Qiuwei Li) 1 Throughout this paper, MATLAB notations are adopted: Q(m, : ), Q(:, k) and Q(i, j) denote the mth row, kth column, and (i, j)th entry of the matrix Q; q(n) denotes the nth entry of the vector q. · 0 is used to count the number of nonzero elements.

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Section: Lenamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimized structured sparse sensing matrices for compressive sensing

et al. 2019

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“…C OMPRESSED sensing (CS) is a popular technique [1], [2], [3], [4] which has been applied in many fields including medical image processing [5], deep learning [6], wireless sensor networks [7], sampling and reconstruction of analog signals [8] and so on. CS techniques can save the storage space of signals, improve the efficiency of processing and reduce the transmission bandwidth while the useful information is well kept.…”

Section: Introductionmentioning

confidence: 99%

Design of Compressed Sensing System With Probability-Based Prior Information

Jiang

Zhu

et al. 2020

IEEE Trans. Multimedia

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This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the dictionary being used, a diagonal weighted matrix is obtained and then the sensing matrix is designed by minimizing a weighted function such that the Gram of the equivalent dictionary is as close to the Gram of dictionary as possible. An analytical solution for the corresponding sensing matrix is derived which leads to low computational complexity. We also exploit this prior information through the sparse recovery stage and propose a probability-driven orthogonal matching pursuit algorithm that improves the accuracy of the recovery. Simulations for synthetic data and application scenarios of surveillance video are carried out to compare the performance of the proposed methods with some existing algorithms. The results reveal that the proposed CS system outperforms existing CS systems.

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“…; Zhu et al . ), dictionary learning (Chen, Ma and Fomel ; Li et al . ) and the deep learning technique (Li et al .…”

Section: Introductionmentioning

confidence: 99%

Low‐rank seismic denoising with optimal rank selection for hankel matrices

Wang

Zhu

2019

Geophysical Prospecting

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A B S T R A C TBased on the fact that the Hankel matrix representing clean seismic data is low rank, low-rank approximation methods have been widely utilized for removing noise from seismic data. A common strategy for real seismic data is to perform the low-rank approximations for small local windows where the events can be approximately viewed as linear. This raises a fundamental question of selecting an optimal rank that best captures the number of events for each local window. Gavish and Donoho proposed a method to select the rank when the noise is independent and identically distributed. Gaussian matrix by analysing the statistical performance of the singular values of the Gaussian matrices. However, such statistical performance is not available for noisy Hankel matrices. In this paper, we adopt the same strategy and propose a rule that computes the number of singular values exceed the median singular value by a multiplicative factor. We suggest a multiplicative factor of 3 based on simulations which mimic the theories underlying Gavish and Donoho in the independent and identically distributed Gaussian setting. The proposed optimal rank selection rule can be incorporated into the classical low-rank approximation method and many other recently developed methods such as those by shrinking the singular values. The low-rank approximation methods with optimally selected rank rule can automatically suppress most of the noise while preserving the main features of the seismic data in each window. Experiments on both synthetic and field seismic data demonstrate the superior performance of the proposed rank selection rule for seismic data denoising.

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On Collaborative Compressive Sensing Systems: The Framework, Design, and Algorithm

Cited by 15 publications

References 60 publications

Optimized structured sparse sensing matrices for compressive sensing

Optimized structured sparse sensing matrices for compressive sensing

Design of Compressed Sensing System With Probability-Based Prior Information

Low‐rank seismic denoising with optimal rank selection for hankel matrices

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