Generalized-cross-validation estimation of the regularization parameters of the subbands in wavelet domain regularized image restoration

A model of regularized image restoration in the wavelet domain is presented in this paper. Separable 2-D wavelets, constructed as the tensorial product of 1-D Daubechies (1990) wavelets of order four (N=4), replace the conventional smoothing filter in the regularized image restoration problem. The regularized solution is computed by minimizing a cost functional which depends upon four regularization parameters (/spl lambda//sub LL/, /spl lambda//sub HL/, /spl lambda//sub LH/ and /spl lambda//sub HH/) corresponding to different subbands. The relationship between the remaining restoration noise and the restored image is given in closed form. A direct solution of the restoration problem is then proposed based upon this relationship. The generalized-cross-validation (GCV) method is applied to estimate the optimal values of the restoration parameters with no prior assumption regarding the original image. Experimental results obtained from the solution of the regularization equation indicate that the proposed method is superior compared to conventional regularized restoration using the Laplacian as a smoothing filter.