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Sparse signals can be recovered from a reduced set of samples by usingcompressive sensing algorithms. In common methods the signal is recovered inthe sparse domain. A method for the reconstruction of sparse signal whichreconstructs the remaining missing samples/measurements is recently proposed.The available samples are fixed, while the missing samples are considered asminimization variables. Recovery of missing samples/measurements is done usingan adaptive gradient-based algorithm in the time domain. A new criterion forthe parameter adaptation in this algorithm, based on the gradient directionangles, is proposed. It improves the algorithm computational efficiency. Atheorem for the uniqueness of the recovered signal for given set of missingsamples (reconstruction variables) is presented. The case when availablesamples are a random subset of a uniformly or nonuniformly sampled signal isconsidered in this paper. A recalculation procedure is used to reconstruct thenonuniformly sampled signal. The methods are illustrated on statisticalexamples.

Reconstruction of Randomly Sampled Sparse Signals Using an Adaptive Gradient Algorithm