The total variation regularized \(L^1\) model for multiscale decomposition. (English) Zbl 1355.49037
Summary: 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.
MSC:
49Q10 | Optimization of shapes other than minimal surfaces |
65K10 | Numerical optimization and variational techniques |
65J22 | Numerical solution to inverse problems in abstract spaces |
68U10 | Computing methodologies for image processing |
94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |