On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis

An approach to sparse signals reconstruction considering its missing measurements/samples as variables is recently proposed. Number and positions of missing samples determine the uniqueness of the solution. It has been assumed that analyzed signals are sparse in the discrete Fourier transform (DFT) domain. A theorem for simple uniqueness check is proposed. Two forms of the theorem are presented, for an arbitrary sparse signal and for an already reconstructed signal. The results are demonstrated on illustrative and statistical examples.