  Sparse signals can be recovered from a reduced set of samples by using
compressive sensing algorithms. In common methods the signal is recovered in
the sparse domain. A method for the reconstruction of sparse signal which
reconstructs the remaining missing samples/measurements is recently proposed.
The available samples are fixed, while the missing samples are considered as
minimization variables. Recovery of missing samples/measurements is done using
an adaptive gradient-based algorithm in the time domain. A new criterion for
the parameter adaptation in this algorithm, based on the gradient direction
angles, is proposed. It improves the algorithm computational efficiency. A
theorem for the uniqueness of the recovered signal for given set of missing
samples (reconstruction variables) is presented. The case when available
samples are a random subset of a uniformly or nonuniformly sampled signal is
considered in this paper. A recalculation procedure is used to reconstruct the
nonuniformly sampled signal. The methods are illustrated on statistical
examples.
