Blind image identification and restoration for noisy blurred images based on discrete sine transform

This paper presents a maximum likelihood (ML) identification and restoration method for noisy blurred images. The unitary discrete sine transform (DST) is employed to decouple the large order spatial state-space representation of the noisy blurred image into a bank of one-dimensional real state-space scalar subsystems. By assuming that the noises are Gaussian distributed processes, the maximum likelihood estimation technique using the expectation-maximization (EM) algorithm is developed to jointly identify the blurring functions, the image model parameters and the noise variances. In order to improve the computational efficiency, the conventional Kalman smoother is incorporated to give the estimates. The identification process also yields the estimates of transformed image data, from which the original image is restored by the inverse DST. The experimental results show the effectiveness of the proposed method and its superiority over the recently proposed spatial domain DFT-based methods.