A proximal decomposition method for solving convex variational inverse problems

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of nonsmooth functions and establish its weak convergence. The algorithm fully decomposes the problem in that it involves each function individually via its own proximity operator. A significant improvement over the methods currently in use in the area of inverse problems is that it is not limited to two nonsmooth functions. Numerical applications to signal and image processing problems are demonstrated.

• Publication year

  2008

• Venue

  Inverse Problems

• Publication date

  2008-07-16

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1088/0266-5611/24/6/065014arXiv 0807.2617
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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