Convexity in source separation: Models, geometry, and algorithms

Source separation or demixing is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these applications, advances in high-throughput sensor technology place demixing algorithms under pressure to accommodate extremely high-dimensional signals, separate an ever larger number of sources, and cope with more sophisticated signal and mixing models. These difficulties are exacerbated by the need for real-time action in automated decision-making systems. Recent advances in convex optimization provide a simple framework for efficiently solving numerous difficult demixing problems. This article provides an overview of the emerging field, explains the theory that governs the underlying procedures, and surveys algorithms that solve them efficiently. We aim to equip practitioners with a toolkit for constructing their own demixing algorithms that work, as well as concrete intuition for why they work

Image formation in synthetic aperture radio telescopes

Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future directions needed for information extraction from future radio telescopes. We describe the imaging process from measurement equation until deconvolution, both as a Fourier inversion problem and as an array processing estimation problem. The latter formulation enables the development of more advanced techniques based on state of the art array processing. We demonstrate the techniques on simulated and measured radio telescope data.Comment: 12 page

Signal processing for guided wave structural health monitoring

The importance of Structural Health Monitoring (SHM) in several industrial fields has been continuously growing in the last few years with the increasing need for the development of systems able to monitor continuously the integrity of complex structures. In order to be competitive with conventional non destructive evaluation techniques, SHM must be able to effectively detect the occurrence of damage in the structure, giving information regarding the damage location. Ultrasonic guided waves offer the possibility of inspecting large areas of structures from a small number of sensor positions. However, inspection of complex structures is difficult as the reflections from different features overlap. Therefore damage detection becomes an extremely challenging problem and robust signal processing is required in order to resolve strongly overlapping echoes. In our work we have considered at first the possibility of employing a deconvolution approach for enhancing the resolution of ultrasonic time traces and the potential and the limitations of this approach for reliable SHM applications have been shown. The effects of noise on the bandwidth of the typical signals in SHM and the effects of frequency dependent phase shifts are the main detrimental issues that strongly reduce the performance of deconvolution in SHM applications. The second part of this thesis is concerned with the evaluation of a subtraction approach for SHM when changes of environmental conditions are taken into account. Temperature changes result in imperfect subtraction even for an undamaged structure, since temperature changes modify the mechanical properties of the material and therefore the velocity of propagation of ultrasonic guided waves. Compensation techniques have previously been used effectively to overcome temperature effects, in order to reduce the residual in the subtraction. In this work the performance of temperature compensation techniques has been evaluated also in the presence of other detrimental effects, such as liquid loading and different temperature responses of materials in adhesive joints. Numerical simulations and experiments have been conducted and it has been shown that temperature compensation techniques can cope in principle with non temperature effects. It is concluded that subtraction approach represents a promising method for reliable Structural Health Monitoring. Nonetheless the feasibility of a subtraction approach for SHM depends on environmental conditions

Coronal Mass Ejection Detection using Wavelets, Curvelets and Ridgelets: Applications for Space Weather Monitoring

Coronal mass ejections (CMEs) are large-scale eruptions of plasma and magnetic feld that can produce adverse space weather at Earth and other locations in the Heliosphere. Due to the intrinsic multiscale nature of features in coronagraph images, wavelet and multiscale image processing techniques are well suited to enhancing the visibility of CMEs and supressing noise. However, wavelets are better suited to identifying point-like features, such as noise or background stars, than to enhancing the visibility of the curved form of a typical CME front. Higher order multiscale techniques, such as ridgelets and curvelets, were therefore explored to characterise the morphology (width, curvature) and kinematics (position, velocity, acceleration) of CMEs. Curvelets in particular were found to be well suited to characterising CME properties in a self-consistent manner. Curvelets are thus likely to be of benefit to autonomous monitoring of CME properties for space weather applications.Comment: Accepted for publication in Advances in Space Research (3 April 2010

Fast and Robust Deconvolution-Based Image Reconstruction for Photoacoustic Tomography in Circular Geometry: Experimental Validation

Photoacoustic tomography (PAT) is a fast-developing biomedical imaging technology suitable for in vivo imaging. PAT in spherical or circular geometry gives good image resolution yet is slow or expensive in signal acquisition and image formation. Reducing the number of detection angles can ameliorate such issues, usually at the expense of image quality. This paper introduces a deconvolution-based algorithm that models the imaging process as a linear and shift-invariant system. As demonstrated by the in vivo experiment, this algorithm not only runs much faster than the back-projection algorithm but also shows stronger robustness in that it provides better image quality when detection angles are sparse. Therefore, this algorithm promises to enable real-time PAT in circular geometry

A Fast DOA Estimation Algorithm Based on Polarization MUSIC

A fast DOA estimation algorithm developed from MUSIC, which also benefits from the processing of the signals' polarization information, is presented. Besides performance enhancement in precision and resolution, the proposed algorithm can be exerted on various forms of polarization sensitive arrays, without specific requirement on the array's pattern. Depending on the continuity property of the space spectrum, a huge amount of computation incurred in the calculation of 4-D space spectrum is averted. Performance and computation complexity analysis of the proposed algorithm is discussed and the simulation results are presented. Compared with conventional MUSIC, it is indicated that the proposed algorithm has considerable advantage in aspects of precision and resolution, with a low computation complexity proportional to a conventional 2-D MUSIC

Gravitational wave radiometry: Mapping a stochastic gravitational wave background

The problem of the detection and mapping of a stochastic gravitational wave background (SGWB), either of cosmological or astrophysical origin, bears a strong semblance to the analysis of CMB anisotropy and polarization. The basic statistic we use is the cross-correlation between the data from a pair of detectors. In order to `point' the pair of detectors at different locations one must suitably delay the signal by the amount it takes for the gravitational waves (GW) to travel to both detectors corresponding to a source direction. Then the raw (observed) sky map of the SGWB is the signal convolved with a beam response function that varies with location in the sky. We first present a thorough analytic understanding of the structure of the beam response function using an analytic approach employing the stationary phase approximation. The true sky map is obtained by numerically deconvolving the beam function in the integral (convolution) equation. We adopt the maximum likelihood framework to estimate the true sky map that has been successfully used in the broadly similar, well-studied CMB map making problem. We numerically implement and demonstrate the method on simulated (unpolarized) SGWB for the radiometer consisting of the LIGO pair of detectors at Hanford and Livingston. We include `realistic' additive Gaussian noise in each data stream based on the LIGO-I noise power spectral density. The extension of the method to multiple baselines and polarized GWB is outlined. In the near future the network of GW detectors, including the Advanced LIGO and Virgo detectors that will be sensitive to sources within a thousand times larger spatial volume, could provide promising data sets for GW radiometry.Comment: 24 pages, 19 figures, pdflatex. Matched version published in Phys. Rev. D - minor change