  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.
