On the Errors in Randomly Sampled Nonsparse Signals Reconstructed With a Sparsity Assumption

An analysis of errors in the reconstruction of approximately sparse and nonsparse noisy signals in the discrete Fourier transform domain is considered in this letter. Signal reconstruction is performed from a reduced set of data, using compressive sensing methods and the sparsity assumption. Random sampling positions in time are considered. Reconstruction results are compared with those obtained with a subset of uniformly sampled signals. A random subset of uniformly sampled data produces better reconstruction results. Theoretical results are statistically confirmed.