Fast High-Dimensional Kernel Filtering

The bilateral and nonlocal means filters are instances of kernel-based filters that are popularly used in image processing. It was recently shown that fast and accurate bilateral filtering of grayscale images can be performed using a low-rank approximation of the kernel matrix. More specifically, based on the eigendecomposition of the kernel matrix, the overall filtering was approximated using spatial convolutions, for which efficient algorithms are available. Unfortunately, this technique cannot be scaled to high-dimensional data such as color and hyperspectral images. This is simply because one needs to compute/store a large matrix and perform its eigendecomposition in this case. We show how this problem can be solved using the Nystr\"om method, which is generally used for approximating the eigendecomposition of large matrices. The resulting algorithm can also be used for nonlocal means filtering. We demonstrate the effectiveness of our proposal for bilateral and nonlocal means filtering of color and hyperspectral images. In particular, our method is shown to be competitive with state-of-the-art fast algorithms, and moreover it comes with a theoretical guarantee on the approximation error

On the Construction of Averaged Deep Denoisers for Image Regularization

Plug-and-Play (PnP) and Regularization by Denoising (RED) are recent paradigms for image reconstruction that can leverage the power of modern denoisers for image regularization. In particular, these algorithms have been shown to deliver state-of-the-art reconstructions using CNN denoisers. Since the regularization is performed in an ad-hoc manner in PnP and RED, understanding their convergence has been an active research area. Recently, it was observed in many works that iterate convergence of PnP and RED can be guaranteed if the denoiser is averaged or nonexpansive. However, integrating nonexpansivity with gradient-based learning is a challenging task -- checking nonexpansivity is known to be computationally intractable. Using numerical examples, we show that existing CNN denoisers violate the nonexpansive property and can cause the PnP iterations to diverge. In fact, algorithms for training nonexpansive denoisers either cannot guarantee nonexpansivity of the final denoiser or are computationally intensive. In this work, we propose to construct averaged (contractive) image denoisers by unfolding ISTA and ADMM iterations applied to wavelet denoising and demonstrate that their regularization capacity for PnP and RED can be matched with CNN denoisers. To the best of our knowledge, this is the first work to propose a simple framework for training provably averaged (contractive) denoisers using unfolding networks

Guided Nonlocal Patch Regularization and Efficient Filtering-Based Inversion for Multiband Fusion

In multiband fusion, an image with a high spatial and low spectral resolution is combined with an image with a low spatial but high spectral resolution to produce a single multiband image having high spatial and spectral resolutions. This comes up in remote sensing applications such as pansharpening~(MS+PAN), hyperspectral sharpening~(HS+PAN), and HS-MS fusion~(HS+MS). Remote sensing images are textured and have repetitive structures. Motivated by nonlocal patch-based methods for image restoration, we propose a convex regularizer that (i) takes into account long-distance correlations, (ii) penalizes patch variation, which is more effective than pixel variation for capturing texture information, and (iii) uses the higher spatial resolution image as a guide image for weight computation. We come up with an efficient ADMM algorithm for optimizing the regularizer along with a standard least-squares loss function derived from the imaging model. The novelty of our algorithm is that by expressing patch variation as filtering operations and by judiciously splitting the original variables and introducing latent variables, we are able to solve the ADMM subproblems efficiently using FFT-based convolution and soft-thresholding. As far as the reconstruction quality is concerned, our method is shown to outperform state-of-the-art variational and deep learning techniques.Comment: Accepted in IEEE Transactions on Computational Imagin

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Mechanism of Mg 2+ -accompanied product release in sugar nucleotidyltransferases

The nucleotidyl transfer reaction, catalyzed by sugar nucleotidyltransferases (SNTs), is assisted by two active site Mg 2+ ions. While studying this reaction using X-ray crystallography, we captured snapshots of the pyrophosphate (product) as it exits along a pocket. Surprisingly, one of the active site Mg 2+ ions remains coordinated to the exiting pyrophosphate. This hints at the participation of Mg 2+ in the process of product release, besides its role in catalyzing nucleotidyl transfer. These observations are further supported by enhanced sampling molecular dynamics simulations. Free energy computations suggest that the product release is likely to be rate limiting in SNTs, and the origin of the high free energy barrier for product release could be traced back to the “slow” conformational change of an Arg residue at the exit end of the pocket. These results establish a dual role for Mg 2+, and propose a general mechanism of product release during the nucleotidyl transfer by SNTs

Structures and activities of archaeal members of the LigD 3′-phosphoesterase DNA repair enzyme superfamily

LigD 3′-phosphoesterase (PE) is a component of the bacterial NHEJ apparatus that performs 3′-end-healing reactions at DNA breaks. The tertiary structure, active site and substrate specificity of bacterial PE are unique vis–à-vis other end-healing enzymes. PE homologs are present in archaea, but their properties are uncharted. Here, we demonstrate the end-healing activities of two archaeal PEs—Candidatus Korarchaeum cryptofilum PE (CkoPE; 117 amino acids) and Methanosarcina barkeri PE (MbaPE; 151 amino acids)—and we report their atomic structures at 1.1 and 2.1 Å, respectively. Archaeal PEs are minimized versions of bacterial PE, consisting of an eight-stranded β barrel and a 310 helix. Their active sites are located in a crescent-shaped groove on the barrel’s outer surface, wherein two histidines and an aspartate coordinate manganese in an octahedral complex that includes two waters and a phosphate anion. The phosphate is in turn coordinated by arginine and histidine side chains. The conservation of active site architecture in bacterial and archaeal PEs, and the concordant effects of active site mutations, underscore a common catalytic mechanism, entailing transition state stabilization by manganese and the phosphate-binding arginine and histidine. Our results fortify the proposal that PEs comprise a DNA repair superfamily distributed widely among taxa

Base and Catalyst-Free Synthesis of Nitrobenzodiazepines via a Cascade NNitroallylation- Intramolecular Aza-Michael Addition involving o-Phenylenediamines and Nitroallylic Acetates

Published ArticleA [4+3] annulation of o-phenylenediamines with primary nitroallylic acetates affords nitrobenzodiazepines (NBDZs) in good to excellent yield. The reaction which proceeds in MeOH at room temperature in the absence of any base or catalyst involves a cascade SN2 Nnitroallylation- intramolecular aza-Michael addition sequence. In the case of mono-N-arylated ophenylenediamines and o-aminobenzamides, the reaction stops at the SN2 stage affording nitroallylic amines. On the other hand, reaction of o-aminobenzamides with secondary nitroallylic acetates delivers SN2’ products. Formation of stable SN2 and SN2’ products provides insights into the reactivity of primary and secondary nitroallylic acetates and also the mechanism of formation of nitrobenzodiazepines

QM/MM Studies of The phenylalanine ammonia-lyase variants helped to understand the mechanistic role of the mutations

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