Combining total variation and wavelet packet approaches for image deblurring

We show two ways to combine wavelet packets and total variation-based deblurring methods. For this purpose, we first recall that it is possible to approximate a convolution by mean of an operator diagonal in a wavelet packet basis. Then, we show two possibilities, which use this property, for combining wavelet packets and total variation approaches. We then show in experiments that, doing this, we can expect to have the advantages of both approaches while avoiding their drawbacks.