Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction

Abstract

We present an extension of the BM3D filter to volumetric data. The proposed algorithm, BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar d-dimensional patches are stacked together in a (d+1)-dimensional array and jointly filtered in transform domain. While in BM3D the basic data patches are blocks of pixels, in BM4D we utilize cubes of voxels, which are stacked into a 4-D "group." The 4-D transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes. Thus, the spectrum of the group is highly sparse, leading to very effective separation of signal and noise through coefficient shrinkage. After inverse transformation, we obtain estimates of each grouped cube, which are then adaptively aggregated at their original locations. We evaluate the algorithm on denoising of volumetric data corrupted by Gaussian and Rician noise, as well as on reconstruction of volumetric phantom data with non-zero phase from noisy and incomplete Fourier-domain (k-space) measurements. Experimental results demonstrate the state-of-the-art denoising performance of BM4D, and its effectiveness when exploited as a regularizer in volumetric data reconstruction.

MRI noise estimation and denoising using non-local PCA

“…This method, based on the Discrete Cosine Transform (DCT), uses high frequency components of a local set of patches to locally estimate the noise level. This noise estimation method is used internally in an adaptive version of the BM4D denoising method (Maggioni and Foi, 2013). We will refer to this adaptive version as ABM4D to differentiate it from the non-adaptive method BM4D.…”

Learning Deep Dictionary for Hyperspectral Image Denoising

“…Robust PCA framework [12] is utilized, and shape-adaptive BM3D [11] is used for denoising each component. (3) BM4D [13]. BM4D is one of the state-of-arts approaches for the volumetric data denoising.…”

A finite-element reciprocity solution for EEG forward modeling with realistic individual head models

“…Diffusion gradient vectors were rotated accordingly [31]. For each diffusion-weighted volume, a non-local mean filter was applied [32] and noise was corrected using power image correction adapted for multi-coil acquisitions [33]. No further corrections were applied to correct for eddy current-induced distortions in the diffusion-weighted volumes because the diffusion sequence did a sufficient job of suppressing them.…”