The Total Variation Regularized L1 Model for Multiscale Decomposition
RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS
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This paper studies the total variation regularization model with an L1 fidelity term TV-L1 for decomposing an image into features of different scales. We first show that the images produced by this model can be formed from the minimizers of a sequence of decoupled geometry sub-problems. Using this result we show that the TV-L1 model is able to separate image features according to their scales, where the scale is analytically defined by the G-value. A number of other properties including the geometric and morphological invariance of the TV-L1 model are also proved and their applications discussed.