Robust and iterative adaptive signal processing

Adaptive signal processing plays an important role in many applications including radar, sonar, acoustics, communications, image processing, speech processing, medical imaging and other fields. The goal of this dissertation is to investigate several adaptive signal processing techniques and their related applications. We focus on adaptive beamforming, ultrasound imaging, Doppler spectrogram analysis and aeroacoustic noise analysis.We first consider the adaptive signal processing techniques in the context of beamforming. Numerous approaches have been proposed in the literature to improve the robustness of the data-adaptive standard Capon beamformer (SCB). One of the most popular and widely used robust adaptive beamforming methods is the diagonal loading approach (as well as its extended versions). However, most of these schemes determine the diagonal loading level either in an ad-hoc way or need user parameters that might be hard to determine in practice. Therefore, user parameter-free approaches are desirable. We present a fully automatic approach to compute the diagonal loading level. In our diagonal loading algorithm, the conventional sample covariance matrix used in the SCB formulation is replaced by an enhanced covariance matrix estimate based on a shrinkage method. The enhanced estimate can be achieved by a general linear combination (GLC), of the sample covariance matrix and an identity matrix in a minimum mean-squared error (MSE) sense. The shrinkage parameters, which are related to the diagonal loading levels of the beamformers, can be calculated from the measurements automatically without the need to specify any user parameters. We have demonstrated that the GLC is very useful in the case of small sample sizes---the case in which the users of adaptive arrays are most interested.We then present a comprehensive review of user parameter-free robust adaptive beamforming algorithms. We provide a thorough evaluation of GLC, its special case convex combination (CC) method, ridge regression Capon beamformers (RRCB), the mid-way (MW) algorithm and several iterative approaches including the iterative adaptive approach (IAA), the maximum likelihood based IAA (referred to as IAA-ML) and the multi-snapshot sparse Bayesian learning (M-SBL) under various scenarios such as coherent, non-coherent and distributed sources, steering vector mismatches, snapshot limitations and low signal-to-noise ratio (SNR) levels. Furthermore, we discuss the computational complexities of the algorithms and provide insights into which algorithm is the best choice under which circumstances.We also consider applying adaptive signal processing techniques to ultrasound imaging. We discuss the challenges in ultrasound imaging applications including the wideband, near-field environment and limited data samples. We then extend GLC and IAA to accommodate those requirements, which result in wideband GLC (WGLC) and wideband IAA (WIAA). Both approaches have been shown to have high resolution, and are robust to the finite sample size problems and other model errors.We then consider Doppler spectrogram analysis. We propose a short-time iterative adaptive approach (ST-IAA) based on IAA to form the Doppler spectrogram. Due to its adaptive character, ST-IAA has much higher frequency resolution and lower sidelobes than its data-independent counterpart, i.e., the conventional short-time Fourier transform (STFT) based approach, and thus ST-IAA provides much more accurate spectrograms. Moreover, a model-order selection tool, the generalized information criterion (GIC) can be used in conjunction with ST-IAA to further improve the spectrogram quality.Finally, we present several iterative adaptive signal processing approaches to aeroacoustic noise analysis. One of the approaches is based on optimizing the maximum likelihood (ML) criterion via using the Newton's method. The other approaches, referred to as the Frobenius norm (FN) and Rank-1 methods, employ the cyclic optimization algorithm to solve the problem. We also derive the Cramer-Rao Bounds (CRB) of the unbiased source power estimates. The proposed methods are evaluated using both simulated and measured data. The numerical examples show that these algorithms significantly outperform the existing least squares approach and provide accurate power estimates even under low SNR conditions. Furthermore, the MSEs of the so-obtained estimates are close to the corresponding CRB, especially when the number of data samples is large. The experimental results show that the power estimates obtained by the proposed approaches are consistent with one another.