A gradient-based approach to optimization of compressed sensing systems

Li, Xiumei; Bai, Huang; Hou, Beiping

doi:10.1016/j.sigpro.2017.04.005

Cited by 18 publications

(13 citation statements)

References 22 publications

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“…From then on, several works have been published for jointly optimizing sensing matrix and dictionary. For example, [24] extended the work of [23] to tensor compressive sensing and the experiments on multi-dimensional signals verified its superiority; [25] mainly concerned the normalization of the incoherent dictionary and the equivalent dictionary for clear physical meaning when optimizing these two matrices. Although these works have tried to optimize the sensing matrix and dictionary of CS system in a joint way, it should be pointed out that the model of (12) is still far away from simultaneously optimizing and .…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

Measurement-Driven Framework With Simultaneous Sensing Matrix and Dictionary Optimization for Compressed Sensing

Bai

2020

IEEE Access

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This paper presents a measurement-driven framework to deal with the compressed sensing (CS) system design problem. Under this novel framework, the sparse coefficient matrix is calculated according to the low-dimension measurements, rather than updated along with the dictionary as in the traditional cases. Moreover, a new cost function is proposed to simultaneously optimize the sensing matrix and dictionary. In order to minimize this cost function, an iterative algorithm is carried out. In every iteration, the solutions of the sensing matrix and dictionary are derived analytically. Experiments are executed with real images, especially medical images. The results demonstrate the superiority of the designed CS system composed of the optimized sensing matrix and dictionary with improved performance for image compression and reconstruction.

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Section: Preliminaries and Related Workmentioning

confidence: 99%

Measurement-Driven Framework With Simultaneous Sensing Matrix and Dictionary Optimization for Compressed Sensing

Bai

2020

IEEE Access

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“…The following result establishes that the sequence generated by Algorithm 1 is a Cauchy sequence and thus the sequence itself is convergent and converges to a stationary point of ρ. Clearly, if the step size is chosen to satisfy (18), the convergence still holds. Thus, we suggest a backtracking method in Appendix D to practically choose η.…”

Section: Convergence Analysismentioning

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%

“…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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“…Also, Duarte-Carvajalino et al [19] took the advantage of an eigenvalue decomposition process followed by a KSVD-based algorithm to optimise the measurement matrix and learn dictionary, respectively. Li et al [ 20] proposed a gradient descent-based algorithm derived for solving the optimal sensing matrix problem. Cleju [21] proposed a novel formulation in the form of a rank-constrained nearest correlation matrix problem.…”

Section: Introductionmentioning

confidence: 99%

Robust optimisation algorithm for the measurement matrix in compressed sensing

Zhou

Sun

Liu

2018

CAAI Transactions on Intelligence Technology

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The measurement matrix which plays an important role in compressed sensing has got a lot of attention. However, the existing measurement matrices ignore the energy concentration characteristic of the natural images in the sparse domain, which can help to improve the sensing efficiency and the construction efficiency. Here, the authors propose a simple but efficient measurement matrix based on the Hadamard matrix, named Hadamard-diagonal matrix (HDM). In HDM, the energy conservation in the sparse domain is maximised. In addition, considering the reconstruction performance can be further improved by decreasing the mutual coherence of the measurement matrix, an effective optimisation strategy is adopted in order to reducing the mutual coherence for better reconstruction quality. The authors conduct several experiments to evaluate the performance of HDM and the effectiveness of optimisation algorithm. The experimental results show that HDM performs better than other popular measurement matrices, and the optimisation algorithm can improve the performance of not only the HDM but also the other popular measurement matrices.

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A gradient-based approach to optimization of compressed sensing systems

Cited by 18 publications

References 22 publications

Measurement-Driven Framework With Simultaneous Sensing Matrix and Dictionary Optimization for Compressed Sensing

Measurement-Driven Framework With Simultaneous Sensing Matrix and Dictionary Optimization for Compressed Sensing

Optimized structured sparse sensing matrices for compressive sensing

Robust optimisation algorithm for the measurement matrix in compressed sensing

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