Parametric analysis of Sparse Signals

The parametric analysis is presented for the sparse signal followed generalized Gaussian distribution (GGD). At first, the properties of GGD signal are discussed. A mathematical formula is established to compute the parameter of sparseness. It is shown that the parameter of Laplacian signal is 1, and that of Gaussian signal is 2. For a given GGD signal, comparing with Laplacian signal and Gaussian signal, we can intuitively know how sparse it is by calculating the sparse parameter. Two examples are given to illustrate the fact that only when the source signals are sufficient sparse, we can (achieve) underdetermined blind source separation (BSS) by sparse representation.