Total variation-based image noise reduction with generalized fidelity function

In this letter, we analyze the relationship between the change in the intensity value and the scale of an image feature, when a generalized function is used as the fidelity term in the total variation-based noise removal scheme. Based on the analysis, we propose a designing method of the fidelity function that results in any desired monotonic relationship between the intensity change and the scale. As an example, we designed a fidelity function that results in a larger contrast between the intensity change of a small scaled feature and that of a large scaled one than the original total variation-based noise removal scheme that uses the L-2 norm as the fidelity function.