An Adaptive Gradient Projection Algorithm for Piecewise Convex Optimization and Its Application in Compressed Spectrum Sensing

Tianjing Wang,Guoqing Liu,Hang Shen,Xiaomei Zhu,Hua Jiang

doi:10.1155/2018/9547934

Tianjing Wang, Guoqing Liu + Show 3 more

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https://doi.org/10.1155/2018/9547934

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Abstract

Signal sparse representation has attracted much attention in a wide range of application fields. A central aim of signal sparse representation is to find a sparse solution with the fewest nonzero entries from an underdetermined linear system, which leads to various optimization problems. In this paper, we propose an Adaptive Gradient Projection (AGP) algorithm to solve the piecewise convex optimization in signal sparse representation. To find a sparser solution, AGP provides an adaptive stepsize to move the iteration solution out of the attraction basin of a suboptimal sparse solution and enter the attraction basin of a sparser solution. Theoretical analyses are used to show its fast convergence property. The experimental results of real-world applications in compressed spectrum sensing show that AGP outperforms the traditional detection algorithms in low signal-to-noise-ratio environments.

Highlights

The marked advances in signal processing in recent years have been driven by the emergence of new signal models and their applications
Signal sparse representation is an effective model for solving real-world problems, such as brain signal processing [1], face recognition [2], compressed spectrum sensing [3], and singing voice separation [4]
When SNR equals to −5 dB, the detection probabilities using Affine Scaling Transformation (AST), Adaptive Gradient Projection (AGP), Iteratively Reweighted l1 minimization (IRL1), and Iteratively Thresholding Method (ITM) improve by 75.47%, 79.25%, 58.49%, and 47.17% compared with Energy Detection (ED)

Summary

Introduction

The marked advances in signal processing in recent years have been driven by the emergence of new signal models and their applications. The piecewise convex optimization (2) can be solved using the existing algorithms, including the Focal Underdetermined System Solver (FOCUSS) [11], the Affine Scaling Transformation (AST) method [12], the Iteratively Reweighted l1 minimization (IRL1) [13], and the Iteratively Thresholding Method (ITM) [14]. The solutions they obtain, may be suboptimal sparse solutions.

Adaptive Gradient Projection Algorithm for Piecewise Convex Optimization

Findings

Conclusions