Compressive sensing of signals sparse in 2D Hermite transform domain

Compressive sensing (CS) of signals that exhibit sparsity in the domain of 2D Hermite transform (HT) is considered. The aim is to provide a successful reconstruction of randomly positioned missing samples. Gradient algorithm originally developed for the case of 1D HT as the domain of sparsity is applied as the reconstruction method, generalized and adapted for the case of signals sparse in 2D HT domain. This reconstruction approach minimizes the sparsity measure, with missing samples observed as minimization variables and updated in a steepest descent manner. Theoretical contributions are verified with numerical results.