The total variation regularized L-1 model for multiscale decomposition

This paper studies the total variation regularization with an L-1 fidelity term (TV-L-1) model 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 subproblems. Using this result we show that the TV-L-1 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-L-1 model are also proved and their applications discussed.