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This paper studies the total variation regularization with an L¹ fidelity term (TV‐L¹) 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‐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.
Yin et al. (Mon,) studied this question.