Adaptive gradient based algorithm for complex sparse signal reconstruction

An adaptive gradient based algorithm for signal reconstruction from a reduced set of samples is considered in the paper. An extension to complex-valued signals is proposed. It has been assumed that the signals are sparse in a transformation domain. The proposed algorithm is based on the previously published algorithm suitable for real-valued signals only. The algorithm is based on the steepest descent method where the measure of signal sparsity is minimized by varying missing signal samples, using a decreasing step size in iterations. The algorithm performances are analyzed and presented through examples.