Sparsity analysis of signals

Abstract In this paper, the signals with generalized Gaussian distribution are considered. A mathematical formula is given to illustrate the sparsity of the signals. According to this formula, the measure of the Laplacian signal is 1, and Gaussian signal is 2. Given a signal, compared with Laplacian signal and Gaussian signal, we can intuitively know how sparse the signal is via its measure. Some examples demonstrate that, if there are no sufficient observed signals (e.g. only three observed signals), one can achieve underdetermined blind source separation (BSS) only for sufficiently sparse source signals (e.g. much sparser than Laplacian signals) by the measure we defined *Supported by National Natural Science Foundation of China (Grant Nos. 60325310, 60505005), Guangdong Province Science Foundation for Program of Research Team (Grant No. 04205783), Guangdong Province Natural Science Foundation (Grant Nos. 05103553, 05006508), and the Specialized Prophasic Basic Research Projects of Ministry of Science a...