A comparative study of two-dimensional modeling methods for electromagnetic scattering data

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 2007.Thesis (Master's) -- Bilkent University, 2007.Includes bibliographical references leaves 60-62.The aim of this research is to model two-dimensional data encountered in electromagnetic scattering problems using model-based parameter estimation techniques. Once a highly accurate model is constructed from a few samples, the model can then be used to interpolate between or extrapolate from the original samples at any desired point and any number of times, thus reducing the amount of data needed to be stored in memory or required to be measured. An added advantage is that the computations required to be carried out on the numerical samples can instead be carried out on the analytical model, which may reduce the computational complexity. It is intuitive that a higher number of terms in the model, increases the accuracy, but additionally it has the unwanted effect of increasing the computational complexity and memory requirement as well. An additional goal, therefore, is to solve the optimization problem of obtaining a model by maximizing the accuracy and minimizing the number of terms. Several modeling techniques are compared in this study, especially those based on matrix pencil methods. Some techniques for optimizing their performance have also been suggested. The pros and cons of each method are also discussed. It is shown that using the suggested techniques provides us with better models, but some pointers are also provided towards investigating more viable alternatives.Srinivasan, Anirudh SM.S

Atomic norm denoising with applications to line spectral estimation

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials. We show that the associated convex optimization problem can be solved in polynomial time via semidefinite programming (SDP). We also show that the SDP can be approximated by an l1-regularized least-squares problem that achieves nearly the same error rate as the SDP but can scale to much larger problems. We compare both SDP and l1-based approaches with classical line spectral analysis methods and demonstrate that the SDP outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.Comment: 27 pages, 10 figures. A preliminary version of this work appeared in the Proceedings of the 49th Annual Allerton Conference in September 2011. Numerous numerical experiments added to this version in accordance with suggestions by anonymous reviewer

Xampling in Ultrasound Imaging

Recent developments of new medical treatment techniques put challenging demands on ultrasound imaging systems in terms of both image quality and raw data size. Traditional sampling methods result in very large amounts of data, thus, increasing demands on processing hardware and limiting the exibility in the post-processing stages. In this paper, we apply Compressed Sensing (CS) techniques to analog ultrasound signals, following the recently developed Xampling framework. The result is a system with significantly reduced sampling rates which, in turn, means significantly reduced data size while maintaining the quality of the resulting images.Comment: 17 pages, 9 Figures. Introduced in SPIE Medical Imaging Conference, Orlando Florida, 201