Recovery of Missing Samples Using Sparse Approximation via a Convex Similarity Measure

In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index, which is convex and error-sensitive. The optimization problem incorporating this criterion, is then solved via Alternating Direction Method of Multipliers (ADMM). Simulation results show the efficiency of the proposed method for missing sample recovery of 1D patch vectors and inpainting of 2D image signals

Multi-GPU maximum entropy image synthesis for radio astronomy

The maximum entropy method (MEM) is a well known deconvolution technique in radio-interferometry. This method solves a non-linear optimization problem with an entropy regularization term. Other heuristics such as CLEAN are faster but highly user dependent. Nevertheless, MEM has the following advantages: it is unsupervised, it has a statistical basis, it has a better resolution and better image quality under certain conditions. This work presents a high performance GPU version of non-gridding MEM, which is tested using real and simulated data. We propose a single-GPU and a multi-GPU implementation for single and multi-spectral data, respectively. We also make use of the Peer-to-Peer and Unified Virtual Addressing features of newer GPUs which allows to exploit transparently and efficiently multiple GPUs. Several ALMA data sets are used to demonstrate the effectiveness in imaging and to evaluate GPU performance. The results show that a speedup from 1000 to 5000 times faster than a sequential version can be achieved, depending on data and image size. This allows to reconstruct the HD142527 CO(6-5) short baseline data set in 2.1 minutes, instead of 2.5 days that takes a sequential version on CPU.Comment: 11 pages, 13 figure

Omniscopes: Large Area Telescope Arrays with only N log N Computational Cost

We show that the class of antenna layouts for telescope arrays allowing cheap analysis hardware (with correlator cost scaling as N log N rather than N^2 with the number of antennas N) is encouragingly large, including not only previously discussed rectangular grids but also arbitrary hierarchies of such grids, with arbitrary rotations and shears at each level. We show that all correlations for such a 2D array with an n-level hierarchy can be efficiently computed via a Fast Fourier Transform in not 2 but 2n dimensions. This can allow major correlator cost reductions for science applications requiring exquisite sensitivity at widely separated angular scales, for example 21cm tomography (where short baselines are needed to probe the cosmological signal and long baselines are needed for point source removal), helping enable future 21cm experiments with thousands or millions of cheap dipole-like antennas. Such hierarchical grids combine the angular resolution advantage of traditional array layouts with the cost advantage of a rectangular Fast Fourier Transform Telescope. We also describe an algorithm for how a subclass of hierarchical arrays can efficiently use rotation synthesis to produce global sky maps with minimal noise and a well-characterized synthesized beam.Comment: Replaced to match accepted PRD version. 10 pages, 9 fig

High dynamic range imaging with a single-mode pupil remapping system : a self-calibration algorithm for redundant interferometric arrays

The correction of the influence of phase corrugation in the pupil plane is a fundamental issue in achieving high dynamic range imaging. In this paper, we investigate an instrumental setup which consists in applying interferometric techniques on a single telescope, by filtering and dividing the pupil with an array of single-mode fibers. We developed a new algorithm, which makes use of the fact that we have a redundant interferometric array, to completely disentangle the astronomical object from the atmospheric perturbations (phase and scintillation). This self-calibrating algorithm can also be applied to any - diluted or not - redundant interferometric setup. On an 8 meter telescope observing at a wavelength of 630 nm, our simulations show that a single mode pupil remapping system could achieve, at a few resolution elements from the central star, a raw dynamic range up to 10^6; depending on the brightness of the source. The self calibration algorithm proved to be very efficient, allowing image reconstruction of faint sources (mag = 15) even though the signal-to-noise ratio of individual spatial frequencies are of the order of 0.1. We finally note that the instrument could be more sensitive by combining this setup with an adaptive optics system. The dynamic range would however be limited by the noise of the small, high frequency, displacements of the deformable mirror.Comment: 11 pages, 7 figures. Accepted for publication in MNRA

A new approach to multi-frequency synthesis in radio interferometry

We present a new approach to multi-frequency synthesis in radio astronomy. Using Bayesian inference techniques, the new technique estimates the sky brightness and the spectral index simultaneously. In principle, the bandwidth of a wide-band observation can be fully exploited for sensitivity and resolution, currently only limited by higher order effects like spectral curvature. Employing this new approach, we further present a multi-frequency extension to the imaging algorithm RESOLVE. In simulations, this new algorithm outperforms current multi-frequency imaging techniques like MS-MF-CLEAN.Comment: 13 pages, 5 fugures, submitted to Astronomy and Astrophysic