Image restoration is an ill posed problem and must be regularized.Usually

the difficulty of regularization lies in avoiding the smoothing of edges while suppressing the noise.In order to preserve the edges of restored image effectively

a general wavelet based edge-preserving regularization scheme and the corresponding solving scheme are proposed.To get rid of the Gibbs effects of restoration algorithms in wavelet domain

the natural(image's) horizontal(vertical) continuity in horizontal(vertical) sub-band together with additioned punishment are employed.Experiments are presented which verified the theoretical results.