Multi-objective Sparse Signal Reconstruction in Compressed Sensing

Abstract

Multi-objective optimization is the task of finding optimal solutions when an optimization problem involves several conflicting objective functions. Multi-objective optimization algorithms try to optimize all the objectives simultaneously and can provide a variety of trade-off solutions among the objectives. There exist numerous algorithms proposed to solve the multi-objective optimization problems in the literature. Some of them are strength Pareto evolutionary algorithm, non-dominated sorting genetic algorithm, multi-objective evolutionary algorithm based on decomposition, and multi-objective particle swarm optimization. Multi-objective optimization algorithms are widely used in many fields. Lately, multi-objective optimization methods have been used in compressed sensing. Compressed sensing is a signal processing technique that can reconstruct a sparse signal at a lower number of measurements than the length of the signal. The development of efficient data acquisition and processing techniques is very important with the rapid development of technology. In addition, an efficient data processing technique affects the speed and the limit of technological developments. The sparse reconstruction algorithms, one of the most important concepts of compressed sensing, can be classified into three main categories as convex relaxation, non-convex relaxation, and greedy algorithms. In addition, multi-objective optimization methods have been started to be used for sparse reconstruction in the literature. The sparse reconstruction problem can be modeled as a bi-objective optimization problem. The objectives are the sparsity function and the measurement loss function. In this study, the multi-objective optimization in general is summarized. Then, basic principles of the compressed sensing method are reviewed. After that, multi-objective sparse reconstruction methods are explained. Finally, a sparse reconstruction method based on non-dominated sorting genetic algorithm II is designed and tested on electrocardiogram signal compression based on compressed sensing. In this way, the effectiveness of the sparse reconstruction technique based on non-dominated sorting genetic algorithm II is examined on a biomedical application. According to the obtained results of the compression process, it is seen that the designed algorithm is effective in optimizing the sparse reconstruction problem.