The Total Variation Regularized L1 Model for Multiscale Decomposition

Wotao Yin, Donald Goldfarb, Stanley J. Osher

Abstract: 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.