Efficient minimization method for a generalized total variation functional

Authors:
Paul Rodríguez;Brendt Wohlberg
Affiliations:
Pontificia Universidad Católica del Perú, Lima, Peru;T-7 Mathematical Modeling and Analysis, Los Alamos National Laboratory, Los Alamos, NM
Venue:
IEEE Transactions on Image Processing
Year:
2009

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Abstract

Replacing the l2 data fidelity term of the standard Total Variation (TV) functional with an l1 data fidelity term has been found to offer a number of theoretical and practical benefits. Efficient algorithms for minimizing this l1-TV functional have only recently begun to be developed, the fastest of which exploit graph representations, and are restricted to the denoising problem. We describe an alternative approach that minimizes a generalized TV functional, including both l2-TV and l1-TV as special cases, and is capable of solving more general inverse problems than denoising (e.g., deconvolution). This algorithm is competitive with the graph-based methods in the denoising case, and is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator.