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Paul Rodríguez and Brendt Wohlberg, "Efficient Minimization Method for a Generalized Total Variation Functional", IEEE Transactions on Image Processing, vol. 18, no. 2, doi:10.1109/TIP.2008.2008420, pp. 322-332, Feb 2009


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 non-trivial forward linear operator.

BibTeX Entry

author = {Paul Rodr\'{i}guez and Brendt Wohlberg},
title = {Efficient Minimization Method for a Generalized Total Variation Functional},
year = {2009},
month = Feb,
urlpdf = {},
journal = {IEEE Transactions on Image Processing},
volume = {18},
number = {2},
doi = {10.1109/TIP.2008.2008420},
pages = {322-332}