Application of multi-objective optimization to blind source separation

Abstract

Several problems in signal processing are addressed by expert systems which take into account a set of priors on the sought signals and systems. For instance, blind source separation is often tackled by means of a mono-objective formulation which relies on a separation criterion associated with a given property of the sought signals (sources). However, in many practical situations, there are more than one property to be exploited and, as a consequence, a set of separation criteria may be used to recover the original signals. In this context, this paper addresses the separation problem by means of an approach based on multi-objective optimization. Differently from the existing methods, which provide only one estimate for the original signals, our proposal leads to a set of solutions that can be utilized by the system user to take his/her decision. Results obtained through numerical experiments over a set of biomedical signals highlight the viability of the proposed approach, which provides estimations closer to the mean squared error solutions compared to the ones achieved via a monoobjective formulation. Moreover, since our proposal is quite general, this work also contributes to encourage future researches to develop expert systems that exploit the multi-objective formulation in different source separation problems.the original sources, which are unknown in real situations. We detail this procedure in Section 4.4.2 It is worth noting that we consider in this paper the determined case, i.e., M = N . 3 In this work, we consider the minimization of cost functions. However, if J(·) must be maximized, the resulting problem can be transformed into minimization by applying the simple transformation max J(·) = min −J(·).

Blind Source Separation with Multi-Objective Optimization for Denoising

“…The solution to this is to find the set of non-dominant points in the minimization problem. The concept of Pareto optimality is used to solve this problem [9].…”

“…Both can be given as examples of evolutionary-based MOO methods. Its enhanced version, known as SPEA2, will also be used in the signal separation techniques that will be presented in this study [9].…”

“…The SPEA is a method developed to find or approximate the Pareto-optimal set for MOO problems [9]. The implementation of the SPEA2 method is explained in Algorithm 1 [24].…”

“…Taking into account Pareto in this optimization, the processing time may take a long time. Therefore, the processing time of MOO tends to be slower than that of single-objective methods [9].…”

“…For the solution of CPP, Independent Component Analysis (ICA), Joint Approximate Diagonalization of Eigenmatrices (JADE), and Nonnegative Matrix Factorization (NMF) algorithms are the most frequently used methods [6]- [8]. Pelegrina, Attux, and Duarte [9] proposed a method to separate mixed signals with the MOO method. Studies have been carried out on the MOO-based ICA method for fMRI data analysis, as well as to remove the noise of the Electroencephalogram (EEG) signal in biomedical signal processing [10]- [12].…”