Random Sampling Using Shannon Interpolation and Poisson Summation Formulae
For researchers in signal processing, this work provides a practical implementation technique for random sampling recovery, but the results are incremental and lack quantitative benchmarks.
This report explores recovery methods for random sampling, using orthogonal matching pursuit and gradient-based total variation, with a fast observation matrix filling technique via Shannon interpolation and Poisson summation. Numerical results for three signal types are presented.
This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast and efficient observation matrix filling technique was implemented by the classic Shannon interpolation and Poisson summation formulae. The numerical results for the trigonometric signal, the Gaussian-modulated sinusoidal pulse, and the square wave were demonstrated and discussed. The work may give some help for future work in theoretical study and practical implementation of the random sampling.