About the use of Lp norms in the problems of unsupervised deconvolution and blind source separation

• Grant number: 17/13025-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: November 01, 2017
• End date: August 31, 2019
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: João Marcos Travassos Romano
• Grantee: Renan Del Buono Brotto
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

One of the most traditional problems in signal processing is the deconvolution, in which the objective is to retrieve a signal that has been distorted by a given system. This problem is still very challenging in its unsupervised version, where the retrieval is carried without knowledge of the system and with access only to some information about the original signal's structure. Among many approaches to this problem, the predictive deconvolution stands out, wherein linear prediction techniques are applied in the unsupervised deconvolution. However, the use of classical linear prediction techniques is limited to minimum-phase systems. In order to deal with this constraint, the Lp predictors appear as potential solutions. These predictors are adjusted by Lp norms and explore the sparse structure of the signals.The problem of unsupervised deconvolution can be generalized into the problem of blind source separation, in which different signals are combined by a mixing system. In this second problem, the goal is to get back the original signals from the observable mixtures. As in deconvolution, the sparsity of the sources can be used as a criterion to the separation task, and this feature can be measured by the Lp norms.In this work, the problem of unsupervised deconvolution as well as the blind source separation will be studied in the context of sparse signals, by means of theoretical approaches and computational simulations, analyzing the potentialities and limitations of Lp norms. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

BROTTO, Renan Del Buono. About lp criteria in predictive deconvolution and blind source separation. 2019. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação Campinas, SP.