Filtering images of more than one channel is challenging in terms of both efficiency and effectiveness. By grouping similar patches to utilize the self-similarity and sparse linear approximation of natural images, recent nonlocal and transformdomain methods have been widely used in color and multispectral image (MSI) denoising. Many related methods focus on the modeling of group level correlation to enhance sparsity, which often resorts to a recursive strategy with a large number of similar patches. The importance of the patch level representation is understated. In this paper, we mainly investigate the influence and potential of representation at patch level by considering a general formulation with block diagonal matrix. We further show that by training a proper global patch basis, along with a local principal component analysis transform in the grouping dimension, a simple transform-threshold-inverse method could produce very competitive results. Fast implementation is also developed to reduce computational complexity. Extensive experiments on both simulated and real datasets demonstrate its robustness, effectiveness and efficiency.

The simultaneous removal of noise and preservation of the integrity of 3-D magnetic resonance (MR) images is a difficult and important task. In this paper, we consider characterizing MR images with 3-D operators, and present a novel 4-D transform-domain method termed 'modified nonlocal tensor-SVD (MNL-tSVD)' for MR image denoising. The proposed method is based on the grouping, hard-thresholding and aggregation paradigms, and can be viewed as a generalized nonlocal extension of tensor-SVD (t-SVD). By keeping MR images in its natural three-dimensional form, and collaboratively filtering similar patches, MNL-tSVD utilizes both the self-similarity property and 3-D structure of MR images to preserve more actual details and minimize the introduction of new artifacts. We show the adaptability of MNL-tSVD by incorporating it into a two-stage denoising strategy with a few adjustments. In addition, analysis of the relationship between MNL-tSVD and current the state-of-the-art 4-D transforms is given. Experimental comparisons over simulated and real brain data sets at different Rician noise levels show that MNL-tSVD can produce competitive performance compared with related approaches.

Amino acids that play a role in binding specificity can be identified with many methods, but few techniques identify the biochemical mechanisms by which they act. To address a part of this problem, we present DeepVASP-E, an algorithm that can suggest electrostatic mechanisms that influence specificity. DeepVASP-E uses convolutional neural networks to classify an electrostatic representation of ligand binding sites into specificity categories. It also uses class activation mapping to identify regions of electrostatic potential that are salient for classification. We hypothesize that electrostatic regions that are salient for classification are also likely to play a biochemical role in achieving specificity. Our findings, on two families of proteins with electrostatic influences on specificity, demonstrate that large salient regions can identify amino acids that have an electrostatic role in binding, and that DeepVASP-E is an effective classifier of ligand binding sites.

Filtering multi-dimensional images such as color images, color videos, multispectral images and magnetic resonance images is challenging in terms of both effectiveness and efficiency. Leveraging the nonlocal self-similarity (NLSS) characteristic of images and sparse representation in the transform domain, the block-matching and 3D filtering (BM3D) based methods show powerful denoising performance. Recently, numerous new approaches with different regularization terms, transforms and advanced deep neural network (DNN) architectures are proposed to improve denoising quality. In this paper, we extensively compare over 60 methods on both synthetic and real-world datasets. We also introduce a new color image and video dataset for benchmarking, and our evaluations are performed from four different perspectives including quantitative metrics, visual effects, human ratings and computational cost. Comprehensive experiments demonstrate: (i) the effectiveness and efficiency of the BM3D family for various denoising tasks, (ii) a simple matrix-based algorithm could produce similar results compared with its tensor counterparts, and (iii) several DNN models trained with synthetic Gaussian noise show state-of-the-art performance on real-world color image and video datasets. Despite the progress in recent years, we discuss shortcomings and possible extensions of existing techniques. Datasets and codes for evaluation are made publicly available at https://github.com/ZhaomingKong/Denoising-Comparison.

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