Pseudo-inverses of difference matrices and their application to sparse signal approximation

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• 作者：Gerlind Plonka^a ; ^{plonka@math.uni-goettingen.de" class="auth_mail" title="E-mail the corresponding author} ; Sebastian Hoffmann^b ; ^{hoffmann@mia.uni-saarland.de" class="auth_mail" title="E-mail the corresponding author} ; Joachim Weickert^b ; ^{weickert@mia.uni-saarland.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A09 ; 35K35 ; 41A15 ; 41A29 ; 94A12
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：503
• 期：Complete
• 页码：26-47
• 全文大小：539 K

文摘

We derive new explicit expressions for the components of Moore–Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial differential equations. The columns of the Moore–Penrose inverse then serve as elements of a dictionary that allow a sparse signal approximation. In order to find a set of suitable data points for signal representation we apply the orthogonal matching pursuit (OMP) method.