A Multiobjective Approach Based on Gaussian Mixture Clustering for Sparse Reconstruction

The application of multiobjective approaches for sparse reconstruction is a relatively new research topic in the area of compressive sensing. Unlike conventional iterative thresholding methods, multiobjective approaches attempt to find a set of solutions called Pareto front (PF) with different sparsity levels. The major focus of the existing sparse multiobjective approaches is to find the knee region of PF, where the
$K$
-sparse solution should reside. However, the strategies in these approaches for finding the knee region of PF are not very reliable due to the sensitivities on the setting of control parameters or noise levels. In this paper, we propose a new strategy based on Gaussian mixture models (GMMs) within a decomposition-based multiobjective framework for sparse reconstruction. The basic idea is to cluster the population found by a chain-based search procedure into two subsets via GMM. One of them with the small values of loss function should include the knee region. Our proposed algorithm was tested on a set of six artificial instance sets at four different noise levels. The experimental results showed that our proposed algorithm is superior to two existing sparse multiobjective approaches and one iterative thresholding algorithm.