Quasi-random sampling for signal recovery

The problem of reconstruction of band-limited signals from nonuniformly sampled and and noisy observations is studied. It is proposed to sample a signal at quasi-random points that form a deterministic sequence, with properties resembling a random variable, being uniformly distributed. Such quasi-random points can be easily and efficiently generated. The reconstruction method based on the modified Whittaker–Shannon cardinal expansion is proposed and its asymptotical properties are examined. In particular, the sufficient conditions for the convergence of the mean integrated squared error are found. The key difference between the proposed reconstruction algorithm and the classical Whittaker–Shannon scheme is in treating the sampling rate and the reconstruction rate differently. This distinction is necessary to ensure consistency of the reconstruction algorithm in the presence of noise.