Fast restoration with edge-preserving regularization

The regularization of the least-squares criterion has been established as an effective approach in image restoration. By, assuming a constant regularization term over the image, restoration based on 2-D FFT´s provides a fast implementation. Unfortunately, this assumption creates significant ringing artifacts on edges as well as blurrier edges in the restored image. On the other hand, shift-variant regularization reduces edge artifacts and provides better quality. However it destroys the structure that makes the use of the 2-D FFT possible, thus no longer allowing the computational efficiency of the FFT. In this paper, we use a new restoration method for the shift-variant regularization approach that can be implemented in a fast and flexible manner. We use a threshold on the regularization terms. In other words, we decompose the blurred image into two independent images. A shift-invariant method is applied to one of them, and a shift-variant method to the other. The shift-variant method is only used on edge pixels, and the shift-invariant method is used on smoother areas. Thus computation is reduced and edge details are preserved. The Sherman-Morrison matrix inversion lemma is used to invert the matrix. Experiments show restored image with sharper edges. Given that edge features are one-dimensional in a two-dimensional image, the computational requirements are also significantly reduced.