5 research outputs found
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Patch diameter limits for tiered subaperture SAR image formation algorithms
Synthetic Aperture Radar image formation algorithms typically use transform techniques that often requires trading between image resolution, algorithm efficiency, and focussed image scene size limits. This is due to assumptions for the data such as simplified (often straight-line) flight paths, simplified imaging geometry, and simplified models for phase functions. Many errors in such assumptions are typically untreatable due to their dependence on both data domain positions and image domain positions. The result is that large scenes often require inefficient multiple image formation iterations, followed by a mosaicking operation of the focussed image patches. One class of image formation algorithms that performs favorably divides the spatial and frequency apertures into subapertures, and perhaps those subapertures into sub-subapertures, and so on, in a tiered subaperture fashion. This allows a gradual shift from data domain into image domain that allows correcting many types of errors that limit other image formation algorithms, even in a dynamic motion environment, thereby allowing larger focussed image patches without mosaicking. This paper presents and compares focussed patch diameter limits for tiered subaperture (TSA) image formation algorithms, for various numbers of tiers of subapertures. Examples are given that show orders-of-magnitude improvement in non-mosaicked focussed image patch size over traditional polar format processing, and that patch size limits increase with the number of tiers of subapertures, although with diminishing returns
Signal processing with Fourier analysis, novel algorithms and applications
Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github