Sparse Bases and Bayesian Inference of Electromagnetic Scattering

Many approaches in CEM rely on the decomposition of complex radiation and scattering behavior with a set of basis vectors. Accurate estimation of the quantities of interest can be synthesized through a weighted sum of these vectors. In addition to basis decompositions, sparse signal processing techniques developed in the CS community can be leveraged when only a small subset of the basis vectors are required to sufficiently represent the quantity of interest. We investigate several concepts in which novel bases are applied to common electromagnetic problems and leverage the sparsity property to improve performance and/or reduce computational burden. The first concept explores the use of multiple types of scattering primitives to reconstruct scattering patterns of electrically large targets. Using a combination of isotropic point scatterers and wedge diffraction primitives as our bases, a 40% reduction in reconstruction error can be achieved. Next, a sparse basis is used to improve DOA estimation. We implement the BSBL technique to determine the angle of arrival of multiple incident signals with only a single snapshot of data from an arbitrary arrangement of non-isotropic antennas. This is an improvement over the current state-of-the-art, where restrictions on the antenna type, configuration, and a priori knowledge of the number of signals are often assumed. Lastly, we investigate the feasibility of a basis set to reconstruct the scattering patterns of electrically small targets. The basis is derived from the TCM and can capture non-localized scattering behavior. Preliminary results indicate that this basis may be used in an interpolation and extrapolation scheme to generate scattering patterns over multiple frequencies

Sparse signal representation based algorithms with application to ultrasonic array imaging

We address one- and two-layer ultrasonic array imaging. We use an array of transducers to inspect the internal structure of a given specimen. In the case of one-layer imaging we also address the problem of mode conversion. We propose a sparse signal representation based method for imaging solid materials in the presence of mode conversion phenomenon. In the case of two-layer imaging we model the signal propagation effect using Huygens principle and Rayleigh-Sommerfeld diffraction formula. We then use this model to develop a sparse signal representation based imaging technique for a test sample immersed in water. Moreover, we develop a new sparse Bayesian technique. In the model that we develop, the reflectivity coefficients of the desired reflectors are nonnegative real numbers and sparse in nature. Therefore, we use Weibull distribution function with two hyperparameters, namely the shape parameter and the scaling parameter, to model the prior distribution function of the reflectivity coefficients of the reflectors. As we show, the Weibull distribution, whose scale parameter obeys the inverse Gamma distribution, will enforce sparsity. We then propose a method for estimating the shape parameter of the Weibull distribution using Mellin transform