Joint nonlinear-quadratic regularization in a wavelet based deconvolution scheme

We describe the improvement of an undecimated wavelet based deconvolution scheme. Both shrinking the wavelets coefficients of the blurred and of the estimated solutions at each resolution level allow a lower smoothing factor in the quadratic Miller-Tikhonov regularization. In addition, an iterative constrained resolution of the normal equations instead of force brute inversion of the stabilized operator contributes to regularization. As a result the excess of smoothness and ringing artifacts near edges and also the noise in flat regions of the image commonly observed in the quadratic regularization are significantly reduced by the proposed approach.