Exact Transform-Domain Variances for Collaborative Filtering of Correlated Noise

Noise as a distortion of signal is an unavoidable part of all imaging. Extreme imaging conditions tend to induce more noise due to low signal energy and faster degradation of the imaging equipment. We focus on modeling and removal of spatially correlated noise, caused by, for example, pixel cross-talk, thermal fluctuations, and variations in sensor response.

Collaborative filters perform denoising through shrinkage on jointly transformed groups of similar patches extracted from the image, crucially depending on the computation of noise variance in the joint transform domain. These variances have conventionally been only crudely approximated, preventing successful collaborative denoising of strongly correlated noise. In the work presented in this thesis, we propose a method for exact computation of the joint transformdomain noise power spectrum, used to improve the conventional algorithms in shrinkage, patch-matching and aggregation of the patch estimates. The improved filters offer state-of-the-art attenuation of correlated noise, with very significant improvements over the conventional versions for strongly structured correlation. We further demonstrate the usage of the exact transform-domain variances in noise estimation, enabling a fully blind denoising setup.

Correlated noise is abundant in many imaging applications. In this work, we specifically consider projections in computed microtomography, commonly corrupted by streak noise with very long-range correlation. We note that the streak noise can, upon a logarithmic transformation, be approximately modeled as additive correlated noise, which we denoise through multiscale frameworks embedding the collaborative filters. The acquisitions are further corrupted by approximately Poissonian noise; as a separate multiscale filtering step, we consider attenuation of this Poissonian component upon a variance stabilization applied on the log-scale data. The presented fully automatic denoisers yield state-of-the-art results in denoising of real microtomography data.