DREAMweb: An online tool for graph-based modeling of NMR protein structure.

The value of accurate protein structural models closely conforming to the experimental data is indisputable. DREAMweb deploys an improved DREAM algorithm, DREAMv2, that incorporates a tighter bound in the constraint set of the underlying optimization approach. This reduces the artifacts while modeling the protein structure by solving the distance-geometry problem. DREAMv2 follows a bottom-up strategy of building smaller substructures for regions with a larger concentration of experimental bounds and consolidating them before modeling the rest of the protein structure. This improves secondary structure conformance in the final models consistent with experimental data. The proposed method efficiently models regions with sparse coverage of experimental data by reducing the possibility of artifacts compared to DREAM. To balance performance and accuracy, smaller substructures ( ∼ 200 $\sim 200$ atoms) are solved in this regime, allowing faster builds for the other parts under relaxed conditions. DREAMweb is accessible as an internet resource. The improvements in results are showcased through benchmarks on 10 structures. DREAMv2 can be used in tandem with any NMR-based protein structure determination workflow, including an iterative framework where the NMR assignment for the NOESY spectra is incomplete or ambiguous. DREAMweb is freely available for public use at http://pallab.cds.iisc.ac.in/DREAM/ and downloadable at https://github.com/niladriranjandas/DREAMv2.git.

Calibrationless parallel magnetic resonance imaging: a joint sparsity model.

State-of-the-art parallel MRI techniques either explicitly or implicitly require certain parameters to be estimated, e.g., the sensitivity map for SENSE, SMASH and interpolation weights for GRAPPA, SPIRiT. Thus all these techniques are sensitive to the calibration (parameter estimation) stage. In this work, we have proposed a parallel MRI technique that does not require any calibration but yields reconstruction results that are at par with (or even better than) state-of-the-art methods in parallel MRI. Our proposed method required solving non-convex analysis and synthesis prior joint-sparsity problems. This work also derives the algorithms for solving them. Experimental validation was carried out on two datasets-eight channel brain and eight channel Shepp-Logan phantom. Two sampling methods were used-Variable Density Random sampling and non-Cartesian Radial sampling. For the brain data, acceleration factor of 4 was used and for the other an acceleration factor of 6 was used. The reconstruction results were quantitatively evaluated based on the Normalised Mean Squared Error between the reconstructed image and the originals. The qualitative evaluation was based on the actual reconstructed images. We compared our work with four state-of-the-art parallel imaging techniques; two calibrated methods-CS SENSE and l1SPIRiT and two calibration free techniques-Distributed CS and SAKE. Our method yields better reconstruction results than all of them.

Improvements on "Fast space-variant elliptical filtering using box splines".

It is well-known that box filters can be efficiently computed using pre-integration and local finite-differences. By generalizing this idea and by combining it with a nonstandard variant of the central limit theorem, we had earlier proposed a constant-time or O(1) algorithm that allowed one to perform space-variant filtering using Gaussian-like kernels. The algorithm was based on the observation that both isotropic and anisotropic Gaussians could be approximated using certain bivariate splines called box splines. The attractive feature of the algorithm was that it allowed one to continuously control the shape and size (covariance) of the filter, and that it had a fixed computational cost per pixel, irrespective of the size of the filter. The algorithm, however, offered a limited control on the covariance and accuracy of the Gaussian approximation. In this paper, we propose some improvements of our previous algorithm.

Fast O1 bilateral filtering using trigonometric range kernels.

It is well known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not scale with the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithms in the image-processing literature. Along with the spatial filter, the edge-preserving bilateral filter involves an additional range kernel. This is used to restrict the averaging to those neighborhood pixels whose intensity are similar or close to that of the pixel of interest. The range kernel operates by acting on the pixel intensities. This makes the averaging process nonlinear and computationally intensive, particularly when the spatial filter is large. In this paper, we show how the O(1) averaging algorithms can be leveraged for realizing the bilateral filter in constant time, by using trigonometric range kernels. This is done by generalizing the idea presented by Porikli, i.e., using polynomial kernels. The class of trigonometric kernels turns out to be sufficiently rich, allowing for the approximation of the standard Gaussian bilateral filter. The attractive feature of our approach is that, for a fixed number of terms, the quality of approximation achieved using trigonometric kernels is much superior to that obtained by Porikli using polynomials.

Fast space-variant elliptical filtering using box splines.

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based upon a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using preintegration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based upon the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.