Reconstruction of signals with sparse representation in optimally dilated Hermite basis

Compressive sensing (CS) provides a set of powerful techniques for the reconstruction of signals with a sparse representation in some particular domain, based on a reduced number of available samples (measurements). The CS application on real-life signals is directly affected by the existence of a basis or a dictionary in which the signal is sparse or highly concentrated (approximately sparse). Motivated by the fact that the time-axis scaling (dilation) factor of Hermite functions (HF) considerably affects the signal sparsity and concentration, in this paper, we propose a CS framework for the signal reconstruction based on a matching pursuit approach using an optimal dilation factor.