In this paper, we propose a recursive filtering algorithm to restore monochromatic images which are corrupted by general dependent additive noise. It is assumed that the equation which describes the image field is not available and a filtering algorithm is obtained using the information provided by the covariance functions of the signal, noise that affects the measurement equation, and the fourth-order moments of the signal. The proposed algorithm is obtained by an innovation approach which provides a simple derivation of the least mean-squared error linear estimators. The estimation of the grey level in each spatial coordinate is made taking into account the information provided by the grey levels located on the row of the pixel to be estimated. The proposed filtering algorithm is applied to restore images which are affected by general signal-dependent additive noise.