Research on the source signal recovery and shape image reconstruction from data with incomplete information based on sparse representation

2014 Fiscal Year Final Research Report

• Project/Area Number: 24500280
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Sensitivity informatics/Soft computing
• Research Institution: The University of Aizu
• Principal Investigator: DING Shuxue 会津大学, コンピュータ理工学部, 教授 (80372829)
• Co-Investigator(Kenkyū-buntansha): OKUYAMA Yuichi 会津大学, コンピュータ理工学部, 准教授 (90404897)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 確率的情報処理 / スパース表現 / Incoherence辞書 / ブラインド信号分離 / 不完全なデータからの復元

Outline of Final Research Achievements

We proposed a new sparsity measure, which is determinant of squared signal matrix. It is smooth and convex function so that have many good features than the conventional ones. We applied it to the blind source separation of nonnegative signal, made effective algorithms. We also researched on the sparse representation. Since this problem is underdetermined system of linear equations, a regularization is necessary. For this purpose we apply a spare constraint to the coefficient, by l1-norm, and a constraint to the dictionary, by incoherence. We use the penalty function method to convert the constrained optimization problem into unconstrained ones. Then we change the problem into a series of iterations of sub optimization problems of quadratic functions and proximal operators, or two different sub optimization problems of quadratic functions. Furthermore, we can solve these sub problems explicitly and obtained closed-form solutions, which leads to algorithms with many good performances.

Free Research Field

信号処理、知能的計算、機械学習