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Affine Invariant Total Variation Models

Balinsky, Helen; Balinsky, Alexander


Keyword(s): total variation; affine restoration; Sobolev inequality; image processing

Abstract: This report relates to the field of image restorations and features extracting from noisy and blurred images. Since their introduction in a classical paper by Rudin, Osher and Fatemi, Total Variation (TV) minimising models have become one of the most popular and successful tools for image restorations. Whilst invariance under affine transformations is very important for many image processing tasks, the total variation functional is not invariant under general affine transformation. In the current report we introduce for the first time a new affine invariant regularization functional which has many properties similar to total variation and can be used for affine invariant denoising and restoration tasks. The explicit formula for calculation of this regularization functional is given.

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