Wideband DOA Estimation with Frequency Decomposition via a Unified GS-WSpSF Framework

A unified group sparsity based framework for wideband sparse spectrum fitting (GS-WSpSF) is proposed for wideband direction-of-arrival (DOA) estimation, which is capable of handling both uncorrelated and correlated sources. Then, by making four different assumptions on a priori knowledge about the sources, four variants under the proposed framework are formulated as solutions to the underdetermined DOA estimation problem without the need of employing sparse arrays. As verified by simulations, improved estimation performance can be achieved by the wideband methods compared with narrowband ones, and adopting more a priori information leads to better performance in terms of resolution capacity and estimation accuracy

Structured Sub-Nyquist Sampling with Applications in Compressive Toeplitz Covariance Estimation, Super-Resolution and Phase Retrieval

Sub-Nyquist sampling has received a huge amount of interest in the past decade. In classical compressed sensing theory, if the measurement procedure satisfies a particular condition known as Restricted Isometry Property (RIP), we can achieve stable recovery of signals of low-dimensional intrinsic structures with an order-wise optimal sample size. Such low-dimensional structures include sparse and low rank for both vector and matrix cases. The main drawback of conventional compressed sensing theory is that random measurements are required to ensure the RIP property. However, in many applications such as imaging and array signal processing, applying independent random measurements may not be practical as the systems are deterministic. Moreover, random measurements based compressed sensing always exploits convex programs for signal recovery even in the noiseless case, and solving those programs is computationally intensive if the ambient dimension is large, especially in the matrix case. The main contribution of this dissertation is that we propose a deterministic sub-Nyquist sampling framework for compressing the structured signal and come up with computationally efficient algorithms. Besides widely studied sparse and low-rank structures, we particularly focus on the cases that the signals of interest are stationary or the measurements are of Fourier type. The key difference between our work from classical compressed sensing theory is that we explicitly exploit the second-order statistics of the signals, and study the equivalent quadratic measurement model in the correlation domain. The essential observation made in this dissertation is that a difference/sum coarray structure will arise from the quadratic model if the measurements are of Fourier type. With these observations, we are able to achieve a better compression rate for covariance estimation, identify more sources in array signal processing or recover the signals of larger sparsity. In this dissertation, we will first study the problem of Toeplitz covariance estimation. In particular, we will show how to achieve an order-wise optimal compression rate using the idea of sparse arrays in both general and low-rank cases. Then, an analysis framework of super-resolution with positivity constraint is established. We will present fundamental robustness guarantees, efficient algorithms and applications in practices. Next, we will study the problem of phase-retrieval for which we successfully apply the sparse array ideas by fully exploiting the quadratic measurement model. We achieve near-optimal sample complexity for both sparse and general cases with practical Fourier measurements and provide efficient and deterministic recovery algorithms. In the end, we will further elaborate on the essential role of non-negative constraint in underdetermined inverse problems. In particular, we will analyze the nonlinear co-array interpolation problem and develop a universal upper bound of the interpolation error. Bilinear problem with non-negative constraint will be considered next and the exact characterization of the ambiguous solutions will be established for the first time in literature. At last, we will show how to apply the nested array idea to solve real problems such as Kriging. Using spatial correlation information, we are able to have a stable estimate of the field of interest with fewer sensors than classic methodologies. Extensive numerical experiments are implemented to demonstrate our theoretical claims

System Identification with Applications in Speech Enhancement

As the increasing popularity of integrating hands-free telephony on mobile portable devices and the rapid development of voice over internet protocol, identification of acoustic systems has become desirable for compensating distortions introduced to speech signals during transmission, and hence enhancing the speech quality. The objective of this research is to develop system identification algorithms for speech enhancement applications including network echo cancellation and speech dereverberation. A supervised adaptive algorithm for sparse system identification is developed for network echo cancellation. Based on the framework of selective-tap updating scheme on the normalized least mean squares algorithm, the MMax and sparse partial update tap-selection strategies are exploited in the frequency domain to achieve fast convergence performance with low computational complexity. Through demonstrating how the sparseness of the network impulse response varies in the transformed domain, the multidelay filtering structure is incorporated to reduce the algorithmic delay. Blind identification of SIMO acoustic systems for speech dereverberation in the presence of common zeros is then investigated. First, the problem of common zeros is defined and extended to include the presence of near-common zeros. Two clustering algorithms are developed to quantify the number of these zeros so as to facilitate the study of their effect on blind system identification and speech dereverberation. To mitigate such effect, two algorithms are developed where the two-stage algorithm based on channel decomposition identifies common and non-common zeros sequentially; and the forced spectral diversity approach combines spectral shaping filters and channel undermodelling for deriving a modified system that leads to an improved dereverberation performance. Additionally, a solution to the scale factor ambiguity problem in subband-based blind system identification is developed, which motivates further research on subbandbased dereverberation techniques. Comprehensive simulations and discussions demonstrate the effectiveness of the aforementioned algorithms. A discussion on possible directions of prospective research on system identification techniques concludes this thesis

The Nested Periodic Subspaces: Extensions of Ramanujan Sums for Period Estimation

In the year 1918, the Indian mathematician Srinivasa Ramanujan proposed a set of sequences called Ramanujan Sums as bases to expand arithmetic functions in number theory. Today, exactly a 100 years later, we will show that these sequences re-emerge as exciting tools in a completely different context: For the extraction of periodic patterns in data. Combined with the state-of-the-art techniques of DSP, Ramanujan Sums can be used as the starting point for developing powerful algorithms for periodicity applications. The primary inspiration for this thesis comes from a recent extension of Ramanujan sums to subspaces known as the Ramanujan subspaces. These subspaces were designed to span any sequence with integer periodicity, and have many interesting properties. Starting with Ramanujan subspaces, this thesis first develops an entire family of such subspace representations for periodic sequences. This family, called Nested Periodic Subspaces due to their unique structure, turns out to be the least redundant sets of subspaces that can span periodic sequences. Three classes of new algorithms are proposed using the Nested Periodic Subspaces: dictionaries, filter banks, and eigen-space methods based on the auto-correlation matrix of the signal. It will be shown that these methods are especially advantageous to use when the data-length is short, or when the signal is a mixture of multiple hidden periods. The dictionary techniques were inspired by recent advances in sparsity based compressed sensing. Apart from the l1 norm based convex programs currently used in other applications, our dictionaries can admit l2 norm formulations that have linear and closed form solutions, even when the systems is under-determined. A new filter bank is also proposed using the Ramanujan sums. This, named the Ramanujan Filter Bank, can accurately track the instantaneous period for signals that exhibit time varying periodic nature. The filters in the Ramanujan Filter Bank have simple integer valued coefficients, and directly tile the period vs time plane, unlike classical STFT (Short Time Fourier Transform) and wavelets, which tile the time-frequency plane. The third family of techniques developed here are a generalization of the classic MUSIC (MUltiple SIgnal Classification) algorithm for periodic signals. MUSIC is one of the most popular techniques today for line spectral estimation. However, periodic signals are not just any unstructured line spectral signals. There is a nice harmonic spacing between the lines which is not exploited by plain MUSIC. We will show that one can design much more accurate adaptations of MUSIC using Nested Periodic Subspaces. Compared to prior variants of MUSIC for the periodicity problem, our approach is much faster and yields much more accurate results for signals with integer periods. This work is also the first extension of MUSIC that uses simple integer valued basis vectors instead of using traditional complex-exponentials to span the signal subspace. The advantages of the new methods are demonstrated both on simulations, as well as real world applications such as DNA micro-satellites, protein repeats and absence seizures. Apart from practical contributions, the theory of Nested Periodic Subspaces offers answers to a number of fundamental questions that were previously unanswered. For example, what is the minimum contiguous data-length needed to be able to identify the period of a signal unambiguously? Notice that the answer we seek is a fundamental identifiability bound independent of any particular period estimation technique. Surprisingly, this basic question has never been answered before. In this thesis, we will derive precise expressions for the minimum necessary and sufficient datalengths for this question. We also extend these bounds to the context of mixtures of periodic signals. Once again, even though mixtures of periodic signals often occur in many applications, aspects such as the unique identifiability of the component periods were never rigorously analyzed before. We will present such an analysis as well. While the above question deals with the minimum contiguous datalength required for period estimation, one may ask a slightly different question: If we are allowed to pick the samples of a signal in a non-contiguous fashion, how should we pick them so that we can estimate the period using the least number of samples? This question will be shown to be quite difficult to answer in general. In this thesis, we analyze a smaller case in this regard, namely, that of resolving between two periods. It will be shown that the analysis is quite involved even in this case, and the optimal sampling pattern takes an interesting form of sparsely located bunches. This result can also be extended to the case of multi-dimensional periodic signals. We very briefly address multi-dimensional periodicity in this thesis. Most prior DSP literature on multi-dimensional discrete time periodic signals assumes the period to be parallelepipeds. But as shown by the artist M. C. Escher, one can tile the space using a much more diverse variety of shapes. Is it always possible to account for such other periodic shapes using the traditional notion of parallelepiped periods? An interesting analysis in this regard is presented towards the end of the thesis.</p

Compressive techniques for sub-Nyquist data acquisition & processing in vibration-based structural health monitoring of engineering structures

Vibration-based structural health monitoring (VSHM) is an automated method for assessing the integrity and performance of dynamically excited structures through processing of structural vibration response signals acquired by arrays of sensors. From a technological viewpoint, wireless sensor networks (WSNs) offer less obtrusive, more economical, and rapid VSHM deployments in civil structures compared to their tethered counterparts, especially in monitoring large-scale and geometrically complex structures. However, WSNs are constrained by certain practical issues related to local power supply at sensors and restrictions to the amount of wirelessly transmitted data due to increased power consumptions and bandwidth limitations in wireless communications. The primary objective of this thesis is to resolve the above issues by considering sub-Nyquist data acquisition and processing techniques that involve simultaneous signal acquisition and compression before transmission. This drastically reduces the sampling and transmission requirements leading to reduced power consumptions up to 85-90% compared to conventional approaches at Nyquist rate. Within this context, the current state-of-the-art VSHM approaches exploits the theory of compressive sensing (CS) to acquire structural responses at non-uniform random sub-Nyquist sampling schemes. By exploiting the sparse structure of the analysed signals in a known vector basis (i.e., non-zero signal coefficients), the original time-domain signals are reconstructed at the uniform Nyquist grid by solving an underdetermined optimisation problem subject to signal sparsity constraints. However, the CS sparse recovery is a computationally intensive problem that strongly depends on and is limited by the sparsity attributes of the measured signals on a pre-defined expansion basis. This sparsity information, though, is unknown in real-time VSHM deployments while it is adversely affected by noisy environments encountered in practice. To efficiently address the above limitations encountered in CS-based VSHM methods, this research study proposes three alternative approaches for energy-efficient VSHM using compressed structural response signals under ambient vibrations. The first approach aims to enhance the sparsity information of vibrating structural responses by considering their representation on the wavelet transform domain using various oscillatory functions with different frequency domain attributes. In this respect, a novel data-driven damage detection algorithm is developed herein, emerged as a fusion of the CS framework with the Relative Wavelet Entropy (RWE) damage index. By processing sparse signal coefficients on the harmonic wavelet transform for two comparative structural states (i.e., damage versus healthy state), CS-based RWE damage indices are retrieved from a significantly reduced number of wavelet coefficients without reconstructing structural responses in time-domain. The second approach involves a novel signal-agnostic sub-Nyquist spectral estimation method free from sparsity constraints, which is proposed herein as a viable alternative for power-efficient WSNs in VSHM applications. The developed method relies on Power Spectrum Blind Sampling (PSBS) techniques together with a deterministic multi-coset sampling pattern, capable to acquire stationary structural responses at sub-Nyquist rates without imposing sparsity conditions. Based on a network of wireless sensors operating on the same sampling pattern, auto/cross power-spectral density estimates are computed directly from compressed data by solving an overdetermined optimisation problem; thus, by-passing the computationally intensive signal reconstruction operations in time-domain. This innovative approach can be fused with standard operational modal analysis algorithms to estimate the inherent resonant frequencies and modal deflected shapes of structures under low-amplitude ambient vibrations with the minimum power, computational and memory requirements at the sensor, while outperforming pertinent CS-based approaches. Based on the extracted modal in formation, numerous data-driven damage detection strategies can be further employed to evaluate the condition of the monitored structures. The third approach of this thesis proposes a noise-immune damage detection method capable to capture small shifts in structural natural frequencies before and after a seismic event of low intensity using compressed acceleration data contaminated with broadband noise. This novel approach relies on a recently established sub-Nyquist pseudo-spectral estimation method which combines the deterministic co-prime sub-Nyquist sampling technique with the multiple signal classification (MUSIC) pseudo-spectrum estimator. This is also a signal-agnostic and signal reconstruction-free method that treats structural response signals as wide-sense stationary stochastic processes to retrieve, with very high resolution, auto-power spectral densities and structural natural frequency estimates directly from compressed data while filtering out additive broadband noise

Blind identification of acoustic systems and enhancement of reverberant speech

Imperial Users onl