A geometrical investigation on the generalized lp/lq norm for blind deconvolution

Application of the generalized lp/lq norm in blind deconvolution has shown good performance for retrieving sparse signals from noisy data. However, the capability of different lp/lq norms to regularize the blind deconvolution has been still less discussed, especially when p is chosen within (0,1]. In this paper, we present a novel geometrical analysis on the generalized lp/lq norm and we also discuss the effects of different choices of p and q on the results of blind deconvolution. It is found that the generalized lp/lq norm can be factorized into a composition of two mappings and several important characteristics of the generalized lp/lq norm can be uncovered through these two mappings. Based on the findings in the geometrical property of the generalized lp/lq norm, several insights for the application of lp/lq norm to blind deconvolution are further discussed in the conclusions.