This paper presents a methodology for the restoration of the visual quality of still images affected by coding noise. This quality restoration is achieved only by considering the additive coding noise and is therefore limited to an adaptive postprocessing filtering. It is based on a model of the human visual system that considers the relationship between visual stimuli and their visibility. This phenomenon known as masking is used as a criterion for the locally adaptive filtering design. An image transformation that yields visual stimuli tuned to the frequency and orientation according to the perceptual model is proposed. It allows a local measure of the masking of each perceptual stimulus considering the contrast between signal and estimated noise. This measure is obtained by analytic filtering. Processing schemes are presented with applications to the discrete cosine transform (DCT) and subband coded images. One proposed solution considers the characteristics of DCT coding noise for the estimation of the noise. Another solution is based on a "blind" neural estimation of the noise characteristics. Experimental results of the proposed approaches show significant improvements of the visual quality, which validates our perceptual model and filtering.