Filtering of images corrupted by multiplicative and white plus coloured additive noises using covariance information

This paper considers the restoration problem of images which are affected by multiple degradations. Under the assumption that the state–space model of the signal to be estimated is unknown, we propose an algorithm for the filtering problem of images which are corrupted by white plus coloured additive noises and multiplicative noise. Using the fact that the autocovariance functions of the signal and coloured noise are known and expressed in semi-degenerated kernel form, and the fact that the first and second-order moments of the multiplicative and white additive noises are also known, the least mean-squared error linear estimator is obtained. The proposed algorithm is applied to an image which has been corrupted by multiplicative and additive noises.