SL0 Reconstruction Algorithm for Compressive Sensing Based on BFGS Quasi Newton Method

Na SUN; Jiwen LIU; Dongliang XIAO

doi:10.11999/JEIT170813

Volume 40 Issue 10

Sep. 2018

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Na SUN, Jiwen LIU, Dongliang XIAO. SL0 Reconstruction Algorithm for Compressive Sensing Based on BFGS Quasi Newton Method[J]. Journal of Electronics & Information Technology, 2018, 40(10): 2408-2414. doi: 10.11999/JEIT170813

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Na SUN, Jiwen LIU, Dongliang XIAO. SL0 Reconstruction Algorithm for Compressive Sensing Based on BFGS Quasi Newton Method[J]. Journal of Electronics & Information Technology, 2018, 40(10): 2408-2414. doi: 10.11999/JEIT170813

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SL0 Reconstruction Algorithm for Compressive Sensing Based on BFGS Quasi Newton Method

doi: 10.11999/JEIT170813

College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China

Funds: The National Natural Science Foundation of China (61271273)

Received Date: 2017-08-16
Rev Recd Date: 2018-07-19

Available Online: 2018-07-26

Publish Date: 2018-10-01

Abstract

Abstract

Smoothed l₀ norm (SL0) algorithm is a compressive sensing reconstruction algorithm based on approximate l₀ norm, which uses the steepest descent method and gradient projection principle, by selecting a decreasing sequence to get the optimal solution. It has the advantages of high matching degree, low computational complexity and without knowing the signal sparsity. However, the iterative direction of steepest descent method is negative gradient direction, which leads to the " sawtooth phenomenon” and the slower convergence speed in the vicinity of the optimal solution. The Newton method has a good convergence speed but has higher requirement of the initial value and needs to calculate the Hessian matrix. The quasi Newton method overcomes this shortcoming and uses BFGS formula to calculate the approximate matrix of the Hessian matrix, it only needs the first derivative information. On the basis of SL0 algorithm and BFGS quasi Newton method, an improved reconstruction algorithm for Compressed Sensing (CS) signal is proposed. The steepest descent method is first used to get an estimated value, and then is taken as the initial value of quasi Newton method, using BFGS method to update the iterative direction until retaining the optimal solution. The simulation results show that the proposed algorithm has great improvement in reconstruction accuracy, peak signal to noise ratio and reconstruction matching degree.
- Compressive Sensing (CS),
- Reconstruction algorithm,
- Smoothed l₀ norm,
- BFGS

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References(22)

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