Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing with Prior Information

Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in the measurement vector leading to a poor performance when the noise no longer follows the Gaussian assumption but, instead, is better characterized by heavier-than-Gaussian tailed distributions. In this paper, we propose a robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse signals in the presence of impulsive noise. To address this problem, we use a Lorentzian cost function instead of the $L_2$ cost function employed by the traditional IHT algorithm. We also modify the algorithm to incorporate prior signal information in the recovery process. Specifically, we study the case of CS with partially known support. The proposed algorithm is a fast method with computational load comparable to the LS based IHT, whilst having the advantage of robustness against heavy-tailed impulsive noise. Sufficient conditions for stability are studied and a reconstruction error bound is derived. We also derive sufficient conditions for stable sparse signal recovery with partially known support. Theoretical analysis shows that including prior support information relaxes the conditions for successful reconstruction. Simulation results demonstrate that the Lorentzian-based IHT algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments. Numerical results also demonstrate that the partially known support inclusion improves the performance of the proposed algorithm, thereby requiring fewer samples to yield an approximate reconstruction.Comment: 28 pages, 9 figures, accepted in IEEE Transactions on Signal Processin

Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey

Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted

Waveform Design for MIMO Radar and SAR Application

Remote sensing applications using radar systems require specific signal processing to obtain high resolution for radar imagery. This high resolution is essential in detection and imaging processing and is provided by using synthetic aperture radar (SAR) processing. This chapter describes the application of the multiple-input multiple-output (MIMO) configuration and the orthogonal frequency-division multiplexing (OFDM) concept to overcome some existing limitations with conventional imaging systems as well as to assess the improvements achieved

Efficient Time of Arrival Calculation for Acoustic Source Localization Using Wireless Sensor Networks

Acoustic source localization is a very useful tool in surveillance and tracking applications. Potential exists for ubiquitous presence of acoustic source localization systems. However, due to several significant challenges they are currently limited in their applications. Wireless Sensor Networks (WSN) offer a feasible solution that can allow for large, ever present acoustic localization systems. Some fundamental challenges remain. This thesis presents some ideas for helping solve the challenging problems faced by networked acoustic localization systems. We make use of a low-power WSN designed specifically for distributed acoustic source localization. Our ideas are based on three important observations. First, sounds emanating from a source will be free of reflections at the beginning of the sound. We make use of this observation by selectively processing only the initial parts of a sound to be localized. Second, the significant features of a sound are more robust to various interference sources. We perform key feature recognition such as the locations of significant zero crossings and local peaks. Third, these features which are compressed descriptors, can also be used for distributed pattern matching. For this we perform basic pattern analysis by comparing sampled signals from various nodes in order to determine better Time Of Arrivals (TOA). Our implementation tests these ideas in a predictable test environment. A complete system for general sounds is left for future wor

Efficient Time of Arrival Calculation for Acoustic Source Localization Using Wireless Sensor Networks

Acoustic source localization is a very useful tool in surveillance and tracking applications. Potential exists for ubiquitous presence of acoustic source localization systems. However, due to several significant challenges they are currently limited in their applications. Wireless Sensor Networks (WSN) offer a feasible solution that can allow for large, ever present acoustic localization systems. Some fundamental challenges remain. This thesis presents some ideas for helping solve the challenging problems faced by networked acoustic localization systems. We make use of a low-power WSN designed specifically for distributed acoustic source localization. Our ideas are based on three important observations. First, sounds emanating from a source will be free of reflections at the beginning of the sound. We make use of this observation by selectively processing only the initial parts of a sound to be localized. Second, the significant features of a sound are more robust to various interference sources. We perform key feature recognition such as the locations of significant zero crossings and local peaks. Third, these features which are compressed descriptors, can also be used for distributed pattern matching. For this we perform basic pattern analysis by comparing sampled signals from various nodes in order to determine better Time Of Arrivals (TOA). Our implementation tests these ideas in a predictable test environment. A complete system for general sounds is left for future wor

Efficient Time of Arrival Calculation for Acoustic Source Localization Using Wireless Sensor Networks

Acoustic source localization is a very useful tool in surveillance and tracking applications. Potential exists for ubiquitous presence of acoustic source localization systems. However, due to several significant challenges they are currently limited in their applications. Wireless Sensor Networks (WSN) offer a feasible solution that can allow for large, ever present acoustic localization systems. Some fundamental challenges remain. This thesis presents some ideas for helping solve the challenging problems faced by networked acoustic localization systems. We make use of a low-power WSN designed specifically for distributed acoustic source localization. Our ideas are based on three important observations. First, sounds emanating from a source will be free of reflections at the beginning of the sound. We make use of this observation by selectively processing only the initial parts of a sound to be localized. Second, the significant features of a sound are more robust to various interference sources. We perform key feature recognition such as the locations of significant zero crossings and local peaks. Third, these features which are compressed descriptors, can also be used for distributed pattern matching. For this we perform basic pattern analysis by comparing sampled signals from various nodes in order to determine better Time Of Arrivals (TOA). Our implementation tests these ideas in a predictable test environment. A complete system for general sounds is left for future wor

Robust Adaptive Generalized Correntropy-based Smoothed Graph Signal Recovery with a Kernel Width Learning

This paper proposes a robust adaptive algorithm for smooth graph signal recovery which is based on generalized correntropy. A proper cost function is defined for this purpose. The proposed algorithm is derived and a kernel width learning-based version of the algorithm is suggested which the simulation results show the superiority of it to the fixed correntropy kernel version of the algorithm. Moreover, some theoretical analysis of the proposed algorithm are provided. In this regard, firstly, the convexity analysis of the cost function is discussed. Secondly, the uniform stability of the algorithm is investigated. Thirdly, the mean convergence analysis is also added. Finally, the complexity analysis of the algorithm is incorporated. In addition, some synthetic and real-world experiments show the advantage of the proposed algorithm in comparison to some other adaptive algorithms in the literature of adaptive graph signal recovery

Real-time flutter identification

The techniques and a FORTRAN 77 MOdal Parameter IDentification (MOPID) computer program developed for identification of the frequencies and damping ratios of multiple flutter modes in real time are documented. Physically meaningful model parameterization was combined with state of the art recursive identification techniques and applied to the problem of real time flutter mode monitoring. The performance of the algorithm in terms of convergence speed and parameter estimation error is demonstrated for several simulated data cases, and the results of actual flight data analysis from two different vehicles are presented. It is indicated that the algorithm is capable of real time monitoring of aircraft flutter characteristics with a high degree of reliability