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It has been known for a while that l1-norm relaxation can in certain cases solve an under-determined system of linear equations. Recently, [5, 10] proved (in a large dimensional and statistical context) that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of the unknown vector then there is a sparsity (number of non-zero elements...
Two new theorems show how deliberately adding quantizer noise can improve statistical signal detection in array-based nonlinear correlation detection even in the case of infinite-variance alpha-stable channel noise. The first theorem gives a necessary and sufficient condition for such quantizer noise to increase the detection probability for a fixed false-alarm probability. The second theorem shows...
It is well known that compressed sensing problems reduce to solving large under-determined systems of equations. If we choose the elements of the compressed measurement matrix according to some appropriate probability distribution and if the signal is sparse enough then the l1 optimization can recover it with overwhelming probability (see, e.g. [4], [6], [7]). In fact, [4], [6], [7] establish (in...
Localizing micro cracks in critical components is crucial in the field of continuous structural health monitoring. In this paper, we utilize several signal processing and machine learning techniques such as hierarchical clustering and support vector machines (SVM) to process multisensor acoustic emission (AE) data generated by the inception and propagation of cracks. We present preliminary laboratory...
This paper considers the problem of target location estimation in a wireless sensor network based on IEEE 802.15.4 radio signals and proposes a novel implementation of the maximum likelihood (ML) location estimator based on the Cross-Entropy (CE) method. In the proposed CE method, the ML criterion is translated into a stochastic approximation problem which can be solved effectively. Simulation results...
We provide a review of independent component analysis (ICA) for complex-valued improper and noncircular random sources. An improper random signal is correlated with its complex conjugate, and a noncircular random signal has a rotationally variant probability distribution. We present methods for ICA using second-order statistics, and higher-order statistics. For ICA based on second-order statistics,...
Complex random signals play an increasingly important role in array, communications, and biomedical signal processing and related fields. However, the mathematical foundations of complex-valued signals and tools developed for handling them are scattered in literature. There appears to be a need for a concise, unified, and rigorous treatment of such topics. In this paper such a treatment is provided...
This paper introduces new hybrid blind equalization algorithms for QAM signals, the first term of which is the constant modulus criterion (CMA) or its extended version (ECMA) and the second are a penalty term that vanishes at constellation points coordinates. Several penalties, based on cosine, Gaussian and polynomial lscr1-norm functions respectively are investigated. Simulations show the effectiveness...
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and show that a block-version of the orthogonal matching pursuit algorithm recovers block k-sparse signals in no more than k steps if the block-coherence is sufficiently small...
A signal processing approach for modeling vehicle trajectory during lane changing driving is discussed. Because individual driving habits are not a deterministic process, we developed a stochastic method. The proposed model consists of two parts: a dynamic system represented by a hidden Markov model and a cognitive distance space derived from the range distance distribution. The first part models...
In a parallel distributed detection in order to design the optimal fusion rule, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probabilities of the hypotheses. Such knowledge is not available in most practical cases. In this paper, we propose a blind technique for the M-ary distributed detection problem. We derive the probability mass...
Sparse decomposition (SD) of a signal on an overcomplete dictionary has recently attracted a lot of interest in signal processing and statistics, because of its potential application in many different areas including compressive sensing (CS). However, in the current literature, the dictionary matrix has generally been assumed to be of full-rank. In this paper, we consider non-full-rank dictionaries...
We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform (fHT). The fHT is a generalization of the Hilbert transform that extends the quadrature phase-shift action of the latter to arbitrary phase-shifts a real shift parameter controls...
In this paper, the main attention is focused on transient property of control input signal, we propose a novel model reference adaptive control scheme for time-continuous single-input single-output linear systems with input saturation. To improve a control performance, a novel estimator using an observer for the output tracking error signal is proposed. Using the estimator, it is shown theoretically...
This paper introduces the generalized Cauchy distribution derived LLp metric. We analyze the properties of the metric from the point of view of robust statistics and relate the metric to the Lp metric, comparing the robustness of the metrics according to their influence functions. The derived metric is employed in robust clustering. To implement the proposed robust clustering method, a robust centroid...
The problem of source localization using a network of sensors is considered. A maximum likelihood estimation (MLE) based approach is adopted. The measurements received at the sensors due to the random phenomenon are spatially correlated and are characterized by a multivariate distribution. Using the theory of copulas, the joint parametric density of sensor observations is obtained assuming only the...
In this paper, a three-dimensional (3-D) orthogonal frequency division multiplexing (OFDM) is introduced. In the new OFDM, a 3-D signal mapper and 2-D inverse discrete Fourier transform are used to allocate 3-D signals to OFDM subchannels and to modulate the signals, respectively. The minimum Euclidean distance of the 3-D signal mapper is much farther than that of the 2-D mapper if both mappers are...
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