Digital Signal Processing with Matlab Examples, Volume 3 by Jose Maria Giron-Sierra

Author:Jose Maria Giron-Sierra
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

2.4.1.5 TV-l1 Approach

It was suggested in [135] to replace the l2 term in the ROF model by a l1 term. This article, year 2004, contains interesting references from the 90s about the fidelity term and how to avoid outliers. According with this approach, the functional to minimize is:

(2.92)

As shown in [135], the l1 norm is well suited to remove salt and pepper noise. Further analysis by [49, 193], shows that the model enjoys interesting properties of morphological invariance and texture extraction by scale, so geometrical features are better preserved. A first, fast algorithm for solving the optimization problem was presented in [12].

All three models, Meyer, Vese-Osher, and TV-l1, were compared by [194] using a uniform computing approach. The three models were solved as second-order cone programs (SCOP). The comparison refers to 1D signals and 2D images. Also, [194] contains a detailed history, with references, of alternatives for solving the three models.

See [109] for a practical treatment of the TV-l1 decomposition, including various examples and a link to software from a web site.

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