MMSE filtering of generalised signal-dependent noise in spatial and shift-invariant wavelet domains

This paper addresses the topic of filtering digital images corrupted by signal-dependent additive white noise. The noise model is fully parametric to take into account different noise generation processes, like speckle and film-grain noise. Noise reduction is first approached as a linear minimum mean square error estimation in the spatial domain, thus extending previous results to the most general signal-dependent white noise model. The same type of estimation is performed in a shift-invariant wavelet domain, in which the absence of decimation of the decomposition avoids the typical ringing/aliasing impairments of critically subsampled wavelet-based denoising schemes. In the former case, filtered pixel values are obtained as adaptive combinations of raw and of local average values, driven by locally computed statistics. In the latter case, detail wavelet coefficients of the noisy image are adaptively shrunk by using local statistics derived from the noisy image and the noise model, before the denoised image is synthesised. Experimental results demonstrate that the proposed approaches take full advantage of the knowledge of the underlying noise model. Furthermore, the multi-resolution algorithm steadily outperforms the spatial counterpart in terms of both SNR increment and of enhancement in visual quality.