Compressive Sensing of Sparse Signals in the Hermite Transform Basis: Analysis and Algorithm for Signal Reconstruction

An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the probability of success in detection of signal components support is determined. Based on the probabilistic analysis, a threshold for the detection of signal components is provided. It is a crucial step in the definition of a simple non-iterative algorithm for compressive sensing signal reconstruction. The derived theoretical concepts are proved on several examples using different statistical tests.