Yin, WotaoGoldfarb, DonaldOsher, Stanley2018-06-182018-06-182006-11Yin, Wotao, Goldfarb, Donald and Osher, Stanley. "The Total Variation Regularized L1 Model for Multiscale Decomposition." (2006) <a href="https://hdl.handle.net/1911/102062">https://hdl.handle.net/1911/102062</a>.https://hdl.handle.net/1911/102062This 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 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.23 ppengTechnical reportTR06-16