60,940 research outputs found

    Distributed and parallel sparse convex optimization for radio interferometry with PURIFY

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    Next generation radio interferometric telescopes are entering an era of big data with extremely large data sets. While these telescopes can observe the sky in higher sensitivity and resolution than before, computational challenges in image reconstruction need to be overcome to realize the potential of forthcoming telescopes. New methods in sparse image reconstruction and convex optimization techniques (cf. compressive sensing) have shown to produce higher fidelity reconstructions of simulations and real observations than traditional methods. This article presents distributed and parallel algorithms and implementations to perform sparse image reconstruction, with significant practical considerations that are important for implementing these algorithms for Big Data. We benchmark the algorithms presented, showing that they are considerably faster than their serial equivalents. We then pre-sample gridding kernels to scale the distributed algorithms to larger data sizes, showing application times for 1 Gb to 2.4 Tb data sets over 25 to 100 nodes for up to 50 billion visibilities, and find that the run-times for the distributed algorithms range from 100 milliseconds to 3 minutes per iteration. This work presents an important step in working towards computationally scalable and efficient algorithms and implementations that are needed to image observations of both extended and compact sources from next generation radio interferometers such as the SKA. The algorithms are implemented in the latest versions of the SOPT (https://github.com/astro-informatics/sopt) and PURIFY (https://github.com/astro-informatics/purify) software packages {(Versions 3.1.0)}, which have been released alongside of this article.Comment: 25 pages, 5 figure

    Graph Spectral Image Processing

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    Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

    Flexible Multi-layer Sparse Approximations of Matrices and Applications

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    The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems

    Single Frame Image super Resolution using Learned Directionlets

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    In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture directional features and to extract edge information along different directions of a set of available high resolution images .This information is used as the training set for super resolving a low resolution input image and the Directionlet coefficients at finer scales of its high-resolution image are learned locally from this training set and the inverse Directionlet transform recovers the super-resolved high resolution image. The simulation results showed that the proposed approach outperforms standard interpolation techniques like Cubic spline interpolation as well as standard Wavelet-based learning, both visually and in terms of the mean squared error (mse) values. This method gives good result with aliased images also.Comment: 14 pages,6 figure

    A sparsity-driven approach to multi-camera tracking in visual sensor networks

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    In this paper, a sparsity-driven approach is presented for multi-camera tracking in visual sensor networks (VSNs). VSNs consist of image sensors, embedded processors and wireless transceivers which are powered by batteries. Since the energy and bandwidth resources are limited, setting up a tracking system in VSNs is a challenging problem. Motivated by the goal of tracking in a bandwidth-constrained environment, we present a sparsity-driven method to compress the features extracted by the camera nodes, which are then transmitted across the network for distributed inference. We have designed special overcomplete dictionaries that match the structure of the features, leading to very parsimonious yet accurate representations. We have tested our method in indoor and outdoor people tracking scenarios. Our experimental results demonstrate how our approach leads to communication savings without significant loss in tracking performance
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