Radar target imaging using time-reversed processing

This thesis investigates and demonstrates the workability of the time-reversed process for radar imaging applications, particularly, for bi-static or multi-static radars. One benefit of the time-reversed process is its ability to reduce the calculation to determine the targetsgas shape. The finite-difference-time-domain (FDTD) method is used to demonstrate the time-reversed process. Following an overview and description of the principles of the time-reversed process, the FDTD method is applied to the wave equation and the time reversed-process in 2-D space. The FDTD numerical model is developed and used for producing fundamental examples on conducting targets. The examples reveal that the time-reversed process can be employed for radar imaging within certain constraints. Finally, conclusions regarding the time-reversed-process are presented and recommendations for future research are provided.http://archive.org/details/radartargetimagi10945973

Multiscale Adaptive Representation of Signals: I. The Basic Framework

We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational efficiency at inference time. It improves classical multi-scale basis such as wavelet frames in terms of coding efficiency. It provides an attractive alternative to dictionary learning-based techniques for low level signal processing tasks, such as compression and denoising, as well as high level tasks, such as feature extraction for object recognition. Connections with deep convolutional networks are also discussed. In particular, the proposed framework reveals a drawback in the commonly used approach for visualizing the activations of the intermediate layers in convolutional networks, and suggests a natural alternative

Nonlinear Acoustics and an Inverse Scattering Problem

Abstract This Ph.D is concerned with wave propagation problems. The main focus is on nonlinear acoustics, looking at sonic boom propagation in a physically realistic atmosphere, whilst a secondary part will look at the problem of landmine detection and how to improve the target detection rates. The work on nonlinear acoustics emerged as a desire to model the behaviour of the sonic booms formed by supersonic aircraft in the atmosphere to see what environmental impact they would have on people and animals on the ground, in terms of the form of the sound waves once they reach the ground. The work on landmine detection originated from a Knowledge Transfer Partner- ship between the University of East Anglia (UEA) and Cobham Technical Services (CTS) organised through the Knowledge Transfer Network (KTN). This partnership took the form of a six month internship with work undertaken afterwards to publish the �ndings of the internship.

Analytical and numerical techniques for wave scattering

In this thesis, we study the mathematical solution of wave scattering problems which describe the behaviour of waves incident on obstacles and are highly relevant to a raft of applications in the aerospace industry. The techniques considered in the present work can be broadly classed into two categories: analytically based methods which use special transforms and functions to provide a near-complete mathematical description of the scattering process, and numerical techniques which select an approximate solution from a general finite-dimensional space of possible candidates. The first part of this thesis addresses an analytical approach to the scattering of acoustic and vortical waves on an infinite periodic arrangement of finite-length flat blades in parallel mean flow. This geometry serves as an unwrapped model of the fan components in turbo-machinery. Our contributions include a novel semi-analytical solution based on the Wiener–Hopf technique that extends previous work by lifting the restriction that adjacent blades overlap, and a comprehensive study of the composition of the outgoing energy flux for acoustic wave scattering on this array of blades. These results provide an insight into the importance of energy conversion between the unsteady vorticity shed from the trailing edges of the cascade blades and the acoustic field. Furthermore, we show that the balance of incoming and outgoing energy fluxes of the unsteady field provides a convenient tool for understanding several interesting scattering symmetries on this geometry. In the second part of the thesis, we focus on numerical techniques based on the boundary integral method which allows us to write the governing equations for zero mean flow in the form of Fredholm integral equations. We study the solution of these integral equations using collocation methods for two-dimensional scatterers with smooth and Lipschitz boundaries. Our contributions are as follows: Firstly, we explore the extent to which least-squares oversampling can improve collocation. We provide rigorous analysis that proves guaranteed convergence for small amounts of oversampling and shows that superlinear oversampling can ensure faster asymptotic convergence rates of the method. Secondly, we examine the computation of the entries in the discrete linear system representing the continuous integral equation in collocation methods for hybrid numerical-asymptotic basis spaces on simple geometric shapes in the context of high-frequency wave scattering. This requires the computation of singular highly-oscillatory integrals and we develop efficient numerical methods that can compute these integrals at frequency-independent cost. Finally, we provide a general result that allows the construction of recurrences for the efficient computation of quadrature moments in a broad class of Filon quadrature methods, and we show how this framework can also be used to accelerate certain Levin quadrature methods.Supported by EPSRC grant EP/L016516/