A Knee Point Driven Particle Swarm Optimization Algorithm for Sparse Reconstruction

Abstract

Sparse reconstruction is a technique to reconstruct sparse signal from a small number of samples. In sparse reconstruction problems, the sparsity and measurement error should be minimized simultaneously, therefore they can be solved by multi-objective optimization algorithms. Most multi-objective optimizers aim to obtain the complete Pareto front. However only solutions in knee region of Pareto front are preferred in sparse reconstruction problems. It is a waste of time to obtain the whole Pareto front. In this paper, a knee point driven multi-objective particle swarm optimization algorithm (KnMOPSO) is proposed to solve sparse reconstruction problems. KnMOPSO aims to find the local part of Pareto front so that it can solve the sparse reconstruction problems fast and accurately. In KnMOPSO personal best particles and global best particle are selected with knee point selection scheme. In addition, solutions which are more likely to be knee points are preferred to others.