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This paper addresses the independent component analysis (ICA) of quaternion random vectors. In particular, we focus on the Gaussian case and therefore only consider the quaternion second-order statistics (SOS), which are given by the covariance matrix and three complementary covariance matrices. First, we derive the necessary and sufficient conditions for the identifiability of the quaternion ICA model, which are based on the definition of the properness profile of a quaternion random variable and more specifically on the concept of rotationally equivalent properness profiles. Second, we show that the maximum-likelihood (ML) approach to the quaternion ICA problem reduces to the approximated joint diagonalization (AJD) of the sample-mean estimates of the covariance and complementary covariance matrices. Unlike the complex case, these four matrices cannot be simultaneously diagonalized in general, and we have to resort to a particular AJD algorithm. The proposed technique, which can be seen as a quasi-Newton method, is based on the local approximation of the nonconvex ML-ICA cost function (a measure of the entropy loss due to the residual correlation among the estimated quaternion sources), and it provides a satisfactory solution of the quaternion ICA model. The performance of the proposed quaternion ML-ICA algorithm, as well as its relationship to the identifiability conditions, are illustrated by means of several numerical examples. [ABSTRACT FROM PUBLISHER]

ℓ0 norm based algorithms have numerous potential applications where a sparse signal is recovered from a small number of measurements. The direct ℓ0 norm optimization problem is NP-hard. In this paper we work with the the smoothed ℓ0 (SL0) approximation algorithm for sparse representation. We give an upper bound on the run-time estimation error. This upper bound is tighter than the previously known bound. Subsequently, we develop a reliable stopping criterion. This criterion is helpful in avoiding the problems due to the underlying discontinuities of the ℓ0 cost function. Furthermore, we propose an alternative optimization strategy, which results in a Newton like algorithm. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of sensing dictionaries. It presents an alteration of greedy algorithms like thresholding or (orthogonal) matching pursuit which improves their performance in finding sparse signal representations in redundant dictionaries while maintaining the same complexity. These algorithms can be split into a sensing and a reconstruction step, and the former will fail to identify correct atoms if the cumulative coherence of the dictionary is too high. We thus modify the sensing step by introducing a special sensing dictionary. The correct selection of components is then determined by the cross cumulative coherence which can be considerably lower than the cumulative coherence. We characterize the optimal sensing matrix and develop a constructive method to approximate it. Finally, we compare the performance of thresholding and OMP using the original and modified algorithms. [ABSTRACT FROM AUTHOR]

Novel low-density signature (LDS) structure is proposed for transmission and detection of symbol-synchronous communication over memoryless Gaussian channel. Given N as the processing gain, under this new arrangement, users' symbols are spread over N chips but virtually only dv < N chips that contain nonzero-values. The spread symbol is then so uniquely interleaved as the sampled, at chip rate, received signal contains the contribution from only dc < K number of users, where K denotes the total number of users in the system. Furthermore, a near-optimum chip-level iterative soft-in-soft-out (SISO) multiuser decoding (MUD), which is based on message passing algorithm (MPA) technique, is proposed to approximate optimum detection by efficiently exploiting the LDS structure. Given β = K/N as the system loading, our simulation suggested that the proposed system alongside the proposed detection technique, in AWGN channel, can achieve an overall performance that is close to single-user performance, even when the system has 200% loading, i.e., when β = 2. Its robustness against near-far effect and its performance behavior that is very similar to optimum detection are demonstrated in this paper. In addition, the complexity required for detection is now exponential to dc instead of K as in conventional code division multiple access (CDMA) structure employing optimum multiuser detector. [ABSTRACT FROM AUTHOR]

This paper examines the problem of target detection by a wireless sensor network. Sensors acquire measurements emitted from the target that are corrupted by noise, and initially make individual decisions about the presence/absence of the target. We propose the local vote decision fusion algorithm, in which sensors first correct their decisions using decisions of neighboring sensors, and then make a collective decision as a network. An explicit formula that approximates the system's decision threshold for a given false alarm rate is derived using limit theorems for random fields, which provides a theoretical performance guarantee for the algorithm. We examine both distance- and nearest-neighbor-based versions of the local vote algorithm for grid and random sensor deployments and show that, in many situations, for a fixed-system false alarm, the local vote correction achieves significantly higher target detection rate than decision fusion based on uncorrected decisions. The algorithm does not depend on the signal model and is shown to be robust to different types of signal decay. We also extend this framework to temporal fusion, where information becomes available over time. [ABSTRACT FROM AUTHOR]