Sparse Approximation Via Iterative Thresholding

The well-known shrinkage technique is still relevant for contemporary signal processing problems over redundant dictionaries. We present theoretical and empirical analyses for two iterative algorithms for sparse approximation that use shrinkage. The GENERAL IT algorithm amounts to a Landweber iteration with nonlinear shrinkage at each iteration step. The BLOCK IT algorithm arises in morphological components analysis. A sufficient condition for which General IT exactly recovers a sparse signal is presented, in which the cumulative coherence function naturally arises. This analysis extends previous results concerning the Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) algorithms to IT algorithms

First observations with a GNSS antenna to radio telescope interferometer

We describe the design of a radio interferometer composed of a Global Navigation Satellite Systems (GNSS) antenna and a Very Long Baseline Interferometry (VLBI) radio telescope. Our eventual goal is to use this interferometer for geodetic applications including local tie measurements. The GNSS element of the interferometer uses a unique software-defined receiving system and modified commercial geodetic-quality GNSS antenna. We ran three observing sessions in 2022 between a 25 m radio telescope in Fort Davis, Texas (FD-VLBA), a transportable GNSS antenna placed within 100 meters, and a GNSS antenna placed at a distance of about 9 km. We have detected a strong interferometric response with a Signal-to-Noise Ratio (SNR) of over 1000 from Global Positioning System (GPS) and Galileo satellites. We also observed natural radio sources including Galactic supernova remnants and Active Galactic Nuclei (AGN) located as far as one gigaparsec, thus extending the range of sources that can be referenced to a GNSS antenna by 18 orders of magnitude. These detections represent the first observations made with a GNSS antenna to radio telescope interferometer. We have developed a novel technique based on a Precise Point Positioning (PPP) solution of the recorded GNSS signal that allows us to extend integration time at 1.5 GHz to at least 20 minutes without any noticeable SNR degradation when a rubidium frequency standard is used.Comment: 33 pages, 19 figure

Sparsity constrained image reconstruction for MRFM

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Blind deconvolution for sparse molecular imaging

This paper considers the image reconstruction problem when the original image is assumed to be sparse and when limited information of the point spread function (PSF) is available. In particular, we are interested in reconstructing the magnetization density given Magnetic Resonance Force Microscopy (MRFM) image data, and an alternating iterative algorithm is presented to solve this problem. Simulations demonstrate its performance not only in the reconstruction of the original image, but also in the recovery of the partially known PSF. In addition, we suggest the introduction of a smoothing penalty on allowable PSFs to improve the reconstruction. Index Terms — Image restoration, Blind deconvolution, Magnetic resonance force microscopy, Sparseness regularization