Tetrolet shrinkage with anisotropic total variation minimization for image approximation

In this paper, an anisotropic total variation (ATV) minimization is combined with the new adaptive tetrolet transform for discontinuity-preserving image processing. In order to suppress the pseudo-Gibbs artefacts and to increase the regularity, the conventional shrinkage results are further processed by a total variation (TV) minimization scheme, in which only the insignificant tetrolet coefficients of the image are changed by the use of ATV constrained projection, instead of previous TV projections. Numerical experiments of piecewise-smooth images show the good performance of the proposed hybrid method to recover the shape of edges and important detailed directional components, in comparison to some existing methods.