## Efficient Minimization Method for a Generalized Total Variation Functional (2009)

Citations: | 11 - 4 self |

### BibTeX

@MISC{Rodríguez09efficientminimization,

author = {Paul Rodríguez and Brendt Wohlberg},

title = { Efficient Minimization Method for a Generalized Total Variation Functional},

year = {2009}

}

### OpenURL

### 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 non-trivial forward linear operator.