A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing

Abolghasemi, Vahid; Ferdowsi, Saideh; Sanei, Saeid

doi:10.1016/j.sigpro.2011.10.012

Cited by 144 publications

(117 citation statements)

References 24 publications

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“…Our approach is inspired by designing optimized projections by using shrinkage process in [21] and gradient descent process in [22]. Consider the following convex set H which contains the ideal ETFs, the deterministic matrix construction problem can be solved by projecting onto H alternatively…”

Section: The Description Of Mcsgd Algorithmmentioning

confidence: 99%

“…where γ ∈[ μ w , 1) is the shrinkage factor, which enables to adjust the shrinkage range of the elements in G. The proposed shrinkage function, the shrinkage function in [21], the component-wise approach in [22] Gaussian random matrix F ∈ R 400×500 is adopted to validate the proposed MCSGD algorithm. The input parameters are fixed as: β = 0.01, iter ext = 200, iter int = 100 and ε = 10 −4 .…”

Section: Find H Using Shrinkage Processmentioning

confidence: 99%

“…In face of the above shortcoming and inspired by [22], we alternatively apply a gradient descent method to solve the second minimization problem and update F. Denote the cost function J = F T F − H 2 F , the minimization problem is solved by the gradient descent process…”

Section: Update F Using Gradient Descent Processmentioning

confidence: 99%

“…Facing the above tradeoff, according to the simulation results in the former subsection, we choose γ = 0.4 as a reasonable choice. Referring to second minimization, the proposed method offers a gradient descent method to update the F which guarantees gradual reduction of cost function J and convergence to a local minimum [22].…”

Section: Mcsgd Analysismentioning

confidence: 99%

“…In addition, a deterministic matrix benefits the energy efficiency of CSS since its elements do not need to be transmitted and it reduces the number of required reports with detection accuracy constraint. Till now, some researchers have focused on the matrix construction [21,22]. Along this research line, we propose a novel shrinkage function and gradient descent method to construct a deterministic matrix, which is of low t-coherence and improves the detection effectiveness and efficiency.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient cooperative compressive spectrum sensing by identifying multi-candidate and exploiting deterministic matrix

Wang

Yan

et al. 2015

EURASIP J. Adv. Signal Process.

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Cooperative spectrum sensing exploits the spatial diversity to improve the detection of occupied channels in cognitive radio networks (CRNs). Cooperative compressive spectrum sensing (CCSS) utilizing the sparsity of channel occupancy further improves the efficiency by reducing the number of reports without degrading detection performance. In this paper, we firstly and mainly propose the referred multi-candidate orthogonal matrix matching pursuit (MOMMP) algorithms to efficiently and effectively detect occupied channels at fusion center (FC), where multi-candidate identification and orthogonal projection are utilized to respectively reduce the number of required iterations and improve the probability of exact identification. Secondly, two common but different approaches based on threshold and Gaussian distribution are introduced to realize the multi-candidate identification. Moreover, to improve the detection accuracy and energy efficiency, we propose the matrix construction based on shrinkage and gradient descent (MCSGD) algorithm to provide a deterministic filter coefficient matrix of low t-average coherence. Finally, several numerical simulations validate that our proposals provide satisfactory performance with higher probability of detection, lower probability of false alarm and less detection time.

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Section: The Description Of Mcsgd Algorithmmentioning

confidence: 99%

Section: Find H Using Shrinkage Processmentioning

confidence: 99%

Section: Update F Using Gradient Descent Processmentioning

confidence: 99%

Section: Mcsgd Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient cooperative compressive spectrum sensing by identifying multi-candidate and exploiting deterministic matrix

Wang

Yan

et al. 2015

EURASIP J. Adv. Signal Process.

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Efficient heterogeneous parallel programming for compressed sensing based direction of arrival estimation

Fisne

Kilic

Güngör

et al. 2021

Concurrency and Computation

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In the direction of arrival (DoA) estimation, typically sensor arrays are used where the number of required sensors can be large depending on the application. With the help of compressed sensing (CS), hardware complexity of the sensor array system can be reduced since reliable estimations are possible by using the compressed measurements where the compression is done by measurement matrices. After the compression, DoAs are reconstructed by using sparsity promoting algorithms such as alternating direction method of multipliers (ADMM). For the given procedure, both the measurement matrix design and the reconstruction algorithm may include computationally intensive operations, which are addressed in this study. The presented simulation results imply the feasibility of the system in real-time processing with energy efficient implementations. We propose employing parallel programming to satisfy the real-time processing requirements. While the measurement matrix design has been accelerated 16× with CPU based parallel version with respect to the fastest serial implementation, ADMM based DoA estimation has been improved 1.1× with GPU based parallel version compared to the fastest CPU parallel implementation. In addition, we achieved, to the best of our knowledge, the first energy-efficient real-time DoA estimation on embedded Jetson GPGPUs in 15 W power consumption without affecting the DoA accuracy performance. K E Y W O R D S compressed sensing, direction of arrival estimation, embedded GPGPU, parallel programming, real time computing INTRODUCTIONIn many engineering applications, the main concern is to solve a linear system with many unknowns and fewer equations. In such systems, infinitely many solutions might satisfy the system and the goal is to find the best one among them. Traditionally, the solution having the minimum energy (i.e., the minimum 𝓁 2 -norm) is selected. Compressed sensing (CS) 1,2 is a signal processing technique that recovers sparse signals from fewer number of measurements. It can be applied to many fields since most natural signals are sparse in some transformation domain. 3 However, the problem of finding the most sparse solution is NP-hard. 4 Instead, CS proposes using 𝓁 1 -norm minimization, which is a well-known sparsifying algorithm leading to convex optimization problems that can be efficiently solved using algorithms based on alternating direction method of multipliers (ADMM). 5 In addition to this novel reconstruction approach, CS theory also enables accurate estimations by using compressed measurements provided that the measurement matrix satisfies some energy-preserving conditions. 1,2 Direction of arrival (DoA) estimation is a well-known research area in which the CS based techniques are commonly used. Typically, sensor arrays are used as the signal impinges on each sensor in different times causing a phase

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A performance comparison of measurement matrices in compressive sensing

Arjoune

Kaabouch

Ghazi

et al. 2018

Int J Communication

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Summary Compressive sensing involves 3 main processes: signal sparse representation, linear encoding or measurement collection, and nonlinear decoding or sparse recovery. In the measurement process, a measurement matrix is used to sample only the components that best represent the signal. The choice of the measurement matrix has an important impact on the accuracy and the processing time of the sparse recovery process. Hence, the design of accurate measurement matrices is of vital importance in compressive sensing. Over the last decade, a number of measurement matrices have been proposed. Therefore, a detailed review of these measurement matrices and a comparison of their performances are strongly needed. This paper explains the foundation of compressive sensing and highlights the process of measurement by reviewing the existing measurement matrices. It provides a 3‐level classification and compares the performance of 8 measurement matrices belonging to 4 different types using 5 evaluation metrics: the recovery error, processing time, recovery time, covariance, and phase transition diagram. The theoretical performance comparison is validated with experimental results, and the results show that the Circulant, Toeplitz, and Hadamard matrices outperform the other measurement matrices.

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A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing

Cited by 144 publications

References 24 publications

Efficient cooperative compressive spectrum sensing by identifying multi-candidate and exploiting deterministic matrix

Efficient cooperative compressive spectrum sensing by identifying multi-candidate and exploiting deterministic matrix

Efficient heterogeneous parallel programming for compressed sensing based direction of arrival estimation

A performance comparison of measurement matrices in compressive sensing

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