Blind image restoration based on complex filtering

In linear image deconvolution problems, the blur operator is usually assumed to be known, but in practice, this information is mostly unavailable. Therefore, image restoration must be done using only the observed noisy and blurred image. Recently, a blind image deconvolution method which utilized a two-dimensional version of the constant-modulus algorithm was proposed, but it had a problem such that as the bit number representing the pixel value increased, the performance of the method decreased. It worked for six- or less-bit images. In the work presented here, we address this problem and develop a solution by using a complex mapping diagram for image values and utilizing a complex-valued adaptive filter. The visual and numerical results show that the proposed method can remove the blur from the degraded image even when the bit number is as high as eight (which is usually the case in practice).