A local spectral inversion of a linearized TV model for denoising and deblurring.

In this paper, we propose a model for denoising and deblurring consisting of a system of linear partial differential equations with locally constant coefficients, obtained as a local linearization of the total variation models. The keypoint of our model is to get the local inversion of the Laplacian operator, which will be done via the Fast Fourier Transform (FFT). Two local schemes will be developed: a pointwise and a piecewise one. We will analyze both, their advantages and their limitations.