Nonlocal transform-domain denoising of volumetric data with groupwise adaptive variance estimation

We propose an extension of the BM4D volumetric filter to the denoising of data corrupted by spatially nonuniform noise. BM4D implements the grouping and collaborative filtering paradigm, where similar cubes of voxels are stacked into a four-dimensional "group". Each group undergoes a sparsifying four-dimensional transform, that exploits the local correlation among voxels in each cube and the nonlocal correlation between corresponding voxels of different cubes. Thus, signal and noise are effectively separated in transform domain. In this work we take advantage of the sparsity induced by the four-dimensional transform to provide a spatially adaptive estimation of the local noise variance by applying a robust median estimator of the absolute deviation to the spectrum of each filtered group. The adaptive variance estimates are then used during coefficients shrinkage. Finally, the inverse four-dimensional transform is applied to the filtered group, and each individual cube estimate is adaptively aggregated at its original location. Experiments on medical data corrupted by spatially varying Gaussian and Rician noise demonstrate the efficacy of the proposed approach in volumetric data denoising. In case of magnetic resonance signals, the adaptive variance estimate can be also used to compensate the estimation bias due to the non-zero-mean errors of the Rician-distributed data.