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Sparse Dictionaries for Continuous-Domain Inverse Problems

T. Debarre, S. Aziznejad, M. Unser

Proceedings of the Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS'19), Toulouse, French Republic, July 1-4, 2019, paper no. 177.



We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functional matched to such signals, and prove that corresponding continuous-domain inverse problems have hybrid spline solutions, i.e., they are sums of splines matched to the regularization operators. We then propose a B-spline-based exact discretization method to solve such problems algorithmically.


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