A Neurodynamic Optimization Method for Recovery of Compressive Sensed Signals With Globally Converged Solution Approximating to l0 Minimization

Finding the optimal solution to the constrained l(0)-norm minimization problems in the recovery of compressive sensed signals is an NP-hard problem and it usually requires intractable combinatorial searching operations for getting the global optimal solution, unless using other objective functions (e.g., the l(1) norm or l(p) norm) for approximate solutions or using greedy search methods for locally optimal solutions (e.g., the orthogonal matching pursuit type algorithms). In this paper, a neurodynamic optimization method is proposed to solve the l(0)-norm minimization problems for obtaining the global optimum using a recurrent neural network (RNN) model. For the RNN model, a group of modified Gaussian functions are constructed and their sum is taken as the objective function for approximating the l(0) norm and for optimization. The constructed objective function sets up a convexity condition under which the neurodynamic system is guaranteed to obtain the globally convergent optimal solution. An adaptive adjustment scheme is developed for improving the performance of the optimization algorithm further. Extensive experiments are conducted to test the proposed approach in this paper and the output results validate the effectiveness of the new method.