Discrete irregular sampling with larger gaps Original Research Article

Discrete irregular sampling is the problem of recovering a band-limited discrete signal from its nonuniformly sampled values. We introduce a new method for discrete irregular sampling. It features a new sampling geometry where the sampling points are chosen to come in pairs. A frequency domain formulation reduces the problem to a system of linear equations for which the matrix is of Toeplitz type and is positive definite as soon as there are enough samples. An explicit estimate of the condition number of that matrix is given under some condition on the maximum sampling gap. This condition allows gaps larger than the Nyquist gap. We recombine the new method and the conjugate method to deduce an efficient iterative reconstruction scheme for band-limited discrete signals. Numerical results are provided to illustrate the efficiency of the method.