Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothedl0Norm

Xiao-Feng Fang,Ying-Qi Li,Jiang-She Zhang

doi:10.1155/2014/416542

Xiao-Feng Fang, Ying-Qi Li + Show 1 more

Open Access

https://doi.org/10.1155/2014/416542

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Abstract

The smoothedl0norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothedl0norm. It introduces a sequence of smoothed functions to approximate thel0norm and approaches the solution using the specific iteration process with the steepest method. In order to choose an appropriate sequence of smoothed function and solve the optimization problem effectively, we employ approximate hyperbolic tangent multiparameter function as the approximation to the big “steep nature” inl0norm. Simultaneously, we propose an algorithm based on minimizing a reweighted approximatel0norm in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a modified quasi-Newton algorithm. The numerical simulation results show that the proposed algorithms yield improved signal reconstruction quality and performance.

Highlights

Sparse representation of signals has been extensively studied for decades
The sparse signal reconstruction (SSR) algorithm based on the optimization of a smoothed approximate l0 norm is studied in [11] where simulation results are compared with corresponding results obtained with several existing SSR
We present a new signal reconstruction algorithm for compressive sensing (CS), which is based on the minimization of a smoothed approximate l0 norm

Summary

Introduction

Sparse representation of signals has been extensively studied for decades. The concept of signal sparsity and l1 norm based on recovery techniques can be traced back to the work of Logan [1] in 1965, Santosa and Symes [2] in 1986, and Donoho and Stark in 1989 [3]. The sparse signal reconstruction (SSR) algorithm based on the optimization of a smoothed approximate l0 norm is studied in [11] where simulation results are compared with corresponding results obtained with several existing SSR algorithms with respect to reconstruction performance and computational complexity. We present a new signal reconstruction algorithm for CS, which is based on the minimization of a smoothed approximate l0 norm. It differs from the previous algorithms in several aspects.

Signal Reconstruction Based on Approximation Function

Simulation Result

Conclusion and Future Work