A geometrical investigation on the generalized l(p)/l(q) norm for blind deconvolution

作者：Jia, Xiaodong; Zhao, Ming^*; Buzza, Matt; Di, Yuan; Lee, Jay

来源：Signal Processing, 2017, 134: 63-69.

DOI：10.1016/j.sigpro.2016.11.018

• Blind deconvolution
• Minimum entropy deconvolution
• Sparsity
• Signal processing

Application of the generalized l(p)/l(q) norm in blind deconvolution has shown good performance for retrieving sparse signals from noisy data. However, the capability of different l(p)/l(q), 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 l(p)/l(q) 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 l(p)/l(q), norm can be factorized into a composition of two mappings and several important characteristics of the generalized l(p)/l(q) norm can be uncovered through these two mappings. Based on the findings in the geometrical property of the generalized l(p)/l(q), norm, several insights for the application of l(p)/l(q) norm to blind deconvolution are further discussed in the conclusions.

• 出版日期2017-5
• 单位西安交通大学