An efficient algorithm for designing projection matrix in compressive sensing based on alternating optimization

Hong, Tao; Bai, Huang; Li, Sheng; Zhu, Zhihui

doi:10.1016/j.sigpro.2015.12.015

Cited by 31 publications

(56 citation statements)

References 23 publications

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“…Thus (0, 0) ∈ lim k→∞ ∂ρ(Φ k , G k ) and we conclude that any convergent subsequence of {W k } converges to a stationary point of (16). Finally, the statement lim k→∞ ρ(W k ) = ρ(W).…”

Section: Appendix B Proof Of Theoremsupporting

confidence: 51%

“…where ξ ∈ [0, 1) is a pre-set threshold and usually chosen as 0 or µ [11,12,14,16] and S L×L denotes a set of real L × L symmetric matrices. Then the sensing matrices proposed in [14,16] are optimized by solving the following optimization problem 3 :…”

Section: Mutual Coherencementioning

confidence: 99%

“…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%

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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: Appendix B Proof Of Theoremsupporting

confidence: 51%

Section: Mutual Coherencementioning

confidence: 99%

Section: Lenamentioning

confidence: 99%

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Optimized structured sparse sensing matrices for compressive sensing

et al. 2019

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“…Similar issue exists for designing a projection (or sensing) matrix in signal processing application. Recent studies have proposed to design a projection matrix such that it improves incoherence properties of equivalent dictionary, and its multiplication by the noise vector results in a vector with small magnitude [38,39,40]. However, it's more challenging to design a preconditioning matrix for an underdetermined regression problem as both sides of the equation, Ψc+e = u, are multiplied by the preconditioning matrix.…”

Section: A Preconditioning Schemementioning

confidence: 99%

A preconditioning approach for improved estimation of sparse polynomial chaos expansions

Alemazkoor

Meidani

2018

Computer Methods in Applied Mechanics and Engineering

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Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this paper, we consider preconditioning the underdetermined system of equations that is to be solved. Premultiplying a linear equation system by a non-singular matrix results in an equivalent equation system, but it can potentially improve the incoherence properties of the resulting preconditioned measurement matrix and lead to a better recovery accuracy. When measurements are noisy, however, preconditioning can also potentially result in a worse signal-to-noise ratio, thereby deteriorating recovery accuracy. In this work, we propose a preconditioning scheme that improves the incoherence properties of measurement matrix and at the same time prevents undesirable deterioration of signal-to-noise ratio. We provide theoretical motivations and numerical examples that demonstrate the promise of the proposed approach in improving the accuracy of estimated polynomial chaos expansions.

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“…To overcome this issue, we suggest an efficient method to optimize the sensing matrix which is robust to the SRE. The proposed method is inspired by the recent results in [10,11,13] for robust sensing matrices, but it differs from these works in which there is no need to tune the trade-off parameter and hence it is more suitable for online learning and dynamic data. The experiments on natural images demonstrate that jointly optimizing the Sensing Matrix and Sparsifying Dictionary (SMSD) on a large dataset has much better performance in terms of signal recovery accuracy than with the ones shown in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Online learning sensing matrix and sparsifying dictionary simultaneously for compressive sensing

Hong

Zhu

2018

Signal Processing

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This paper considers the problem of simultaneously learning the Sensing Matrix and Sparsifying Dictionary (SMSD) on a large training dataset. To address the formulated joint learning problem, we propose an online algorithm that consists of a closed-form solution for optimizing the sensing matrix with a fixed sparsifying dictionary and a stochastic method for learning the sparsifying dictionary on a large dataset when the sensing matrix is given. Benefiting from training on a large dataset, the obtained compressive sensing (CS) system by the proposed algorithm yields a much better performance in terms of signal recovery accuracy than the existing ones. The simulation results on natural images demonstrate the effectiveness of the suggested online algorithm compared with the existing methods.

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An efficient algorithm for designing projection matrix in compressive sensing based on alternating optimization

Cited by 31 publications

References 23 publications

Optimized structured sparse sensing matrices for compressive sensing

Optimized structured sparse sensing matrices for compressive sensing

A preconditioning approach for improved estimation of sparse polynomial chaos expansions

Online learning sensing matrix and sparsifying dictionary simultaneously for compressive sensing

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