Optimized structured sparse sensing matrices for compressive sensing

Hong, Tao; Xiao, Li; Zhu, Zhihui; Li, Qiuwei

doi:10.1016/j.sigpro.2019.02.004

Cited by 19 publications

(21 citation statements)

References 50 publications

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“…For the particular case of applying CS in a transformed domain (as in this work), the fundamental aspect for the design of the measurement projections is the mutual coherence between the basis matrix

and the resulting projection matrix

[ 17 ], which can be defined as:

i.e., as the largest absolute inner product between any two columns of the matrices

and

. Several works have addressed the design of the projection matrix considering both random projections of the sparse data [ 17 , 18 , 33 , 34 ] or more structured dictionaries [ 35 , 36 , 37 , 38 , 39 ].…”

Section: Cs Formulationmentioning

confidence: 99%

Coded Aperture Hyperspectral Image Reconstruction

García-Sánchez

Fresnedo

González-Coma

et al. 2021

Sensors

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In this work, we study and analyze the reconstruction of hyperspectral images that are sampled with a CASSI device. The sensing procedure was modeled with the help of the CS theory, which enabled efficient mechanisms for the reconstruction of the hyperspectral images from their compressive measurements. In particular, we considered and compared four different type of estimation algorithms: OMP, GPSR, LASSO, and IST. Furthermore, the large dimensions of hyperspectral images required the implementation of a practical block CASSI model to reconstruct the images with an acceptable delay and affordable computational cost. In order to consider the particularities of the block model and the dispersive effects in the CASSI-like sensing procedure, the problem was reformulated, as well as the construction of the variables involved. For this practical CASSI setup, we evaluated the performance of the overall system by considering the aforementioned algorithms and the different factors that impacted the reconstruction procedure. Finally, the obtained results were analyzed and discussed from a practical perspective.

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and the resulting projection matrix

[ 17 ], which can be defined as:

i.e., as the largest absolute inner product between any two columns of the matrices

and

Section: Cs Formulationmentioning

confidence: 99%

Coded Aperture Hyperspectral Image Reconstruction

García-Sánchez

Fresnedo

González-Coma

et al. 2021

Sensors

View full text Add to dashboard Cite

show abstract

“…However, it is difficult to verify whether a given sensing matrix satisfies RIP. Another relatively simple property is the mutual coherence [15][16][17][18][19][20]. The coherence of matrix A means the maximum absolute correlation between different columns of A. Gaussian and Bernoulli matrices are widely used due to their entries being generated by an independent identically distributed (i.i.d.)…”

Section: Introductionmentioning

confidence: 99%

“…The recent growing trend involves replacing the conventional random sensing matrices by optimized ones in order to enhance CS performance further [ 15 , 16 , 17 , 18 , 19 ]. Some conditions have been put forth to evaluate the qualities of a sensing matrix to guarantee exact signal recovery.…”

Section: Introductionmentioning

confidence: 99%

“…However, it shows low recovery accuracy in the CS system when using the class of matrices as a sensing matrix. In order to improve the CS performance, researchers attempt to optimize the sensing matrix with the hope of increasing the reconstruction probability and taking a fewer number of measurements [ 15 , 16 , 17 , 18 ]. Elad proposed an optimized algorithm that iteratively minimizes the t-averaged mutual coherence using shrinkage operation by singular value decomposition (SVD) [ 15 ].…”

Section: Introductionmentioning

confidence: 99%

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Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka–Malmquist Functions

Sheng

Fang

et al. 2021

Sensors

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Compressed sensing (CS) has been proposed to improve the efficiency of signal processing by simultaneously sampling and compressing the signal of interest under the assumption that the signal is sparse in a certain domain. This paper aims to improve the CS system performance by constructing a novel sparsifying dictionary and optimizing the measurement matrix. Owing to the adaptability and robustness of the Takenaka–Malmquist (TM) functions in system identification, the use of it as the basis function of a sparsifying dictionary makes the represented signal exhibit a sparser structure than the existing sparsifying dictionaries. To reduce the mutual coherence between the dictionary and the measurement matrix, an equiangular tight frame (ETF) based iterative minimization algorithm is proposed. In our approach, we modify the singular values without changing the properties of the corresponding Gram matrix of the sensing matrix to enhance the independence between the column vectors of the Gram matrix. Simulation results demonstrate the promising performance of the proposed algorithm as well as the superiority of the CS system, designed with the constructed sparsifying dictionary and the optimized measurement matrix, over existing ones in terms of signal recovery accuracy.

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“…However, the above alternating optimization algorithm does not consider the possible structural constraints of the measurement matrix itself, so the structural properties of the measurement matrix itself will be destroyed after optimization. On the premise of considering the structural properties of the matrix, the literature [19] proposed an alternating optimization algorithm for sparse measurement matrices, and the literature [20] proposed an alternating optimization algorithm for cyclic matrices, but both algorithms are not applicable to the bipolar Toeplitz measurement matrix.…”

Section: Introductionmentioning

confidence: 99%

A Novel Optimization Method for Bipolar Chaotic Toeplitz Measurement Matrix in Compressed Sensing

et al. 2021

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In this paper, a bipolar chaotic Toeplitz measurement matrix optimization algorithm for alternating optimization is presented. The construction of measurement matrices is one of the key techniques for compressive sensing from theory to engineering applications. Recent studies have shown that bipolar chaotic Toeplitz matrices, constructed by combining the intrinsic determinism of bipolar chaotic sequences with the advantages of Toeplitz matrices, have significant advantages over other measurement matrices in terms of memory overhead, computational complexity, and hard implementation. However, problems such as strong correlation and large interdependence coefficients between measurement matrices and sparse dictionaries may still exist in practical applications. To address this problem, we propose a new bipolar chaotic Toeplitz measurement matrix alternating optimization algorithm. Firstly, by introducing the structure matrix, the optimization problem of the measurement matrix is transformed into the optimization problem of the generating sequence, thus ensuring that the optimization process does not destroy the structural properties of the matrix; then, constraints are added to the values of the generating sequence during the optimization process, so that the optimized measurement matrix still maintains the bipolar properties. Finally, the effectiveness of the optimization algorithm in this paper is verified by simulation experiments. The experimental results show that the optimized bipolar chaotic Toeplitz measurement matrix can effectively reduce the reconstruction error and improve the reconstruction probability.

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Optimized structured sparse sensing matrices for compressive sensing

Cited by 19 publications

References 50 publications

Coded Aperture Hyperspectral Image Reconstruction

Coded Aperture Hyperspectral Image Reconstruction

Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka–Malmquist Functions

A Novel Optimization Method for Bipolar Chaotic Toeplitz Measurement Matrix in Compressed Sensing

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