An optimal Tikhonov regularized image restoration algorithm

As the degraded image was recovered with regularization method, the blurred mtrix is a block circulant matrix which can be diagonalized by two dimension Fourier matrix, if the image boundary meets the periodic conditions. The restored image can be obtained by applying two dimensional discrete Fourier transform and its inverse transform. In practice, the regularization parameter affects restored result. For blurred image, the plot of MSE and ISNR as a function of regularization parameter was obtained by least squares fitting. selecting the arithmetic mean of minimum MSE point and maximum ISNR point as the optimal parameter, the corresponding restored image reach or close to the optimal MSE and ISNR.