Using evolutionary programming for reconstruction of an irregularly sampled bandlimited sequence

The problem of reconstructing an irregularly sampled discrete-time band-limited signal with unknown sampling locations can be analyzed using both geometric and algebraic approaches. This problem can be solved using iterative and non-iterative techniques including the cyclic coordinate approach and the random search method. When the spectrum of the given signal is band-limited to 'L' coefficients, the algebraic structure underlying the signal can be dealt using subspace techniques and a method is suggested to classify the solutions based on this approach. We numerically solve the Irregular Sampling at Unknown Locations (ISUL) problem by considering it as a combinatorial optimization problem. The exhaustive search method to determine the optimum solution is computationally intensive. The need for a more efficient optimization technique to save computational complexity leads us to propose Evolutionary Programming as a stochastic optimization technique. Evolutionary algorithms, based on the models of natural evolution were originally developed as a method to evolve finite-state machines for solving time series prediction tasks and were later extended to parameter optimization problems. The solution space is modeled as a population of individuals, and the search for the optimum solution is obtained by evolving to the best individual in the population. We propose an Evolutionary Programming (EP) based method to converge to the global optimum and obtain the set of sampling locations for the given irregularly sampled signal. The results obtained by EP are compared with the Random Search and Cyclic Coordinate descent algorithms.