Mathematical analysis of a model which combines total variation and wavelet for image restoration 1

Abstract

We give a mathematical analysis of a model previously introduced for image restoration. This model combines wavelet approaches and total variation approaches in a natural way. We prove the existence of a solution to the model. Then we show a way to approximate it in such a way that the approximation can be computed (this is done by penalization). We also show a simple experiment which illustrates why the model seems promising.