Number Of Approximating Terms Research Articles

Generalized Frequency-Domain SAR Processing

The range-Doppler algorithm and the chirp-scaling algorithm (CSA) process synthetic aperture radar (SAR) data with approximations to ideal SAR processing. These approximations are invalid for data from systems with wide beamwidths, large bandwidths, and/or low center frequencies. While simple and efficient, these frequency-domain methods are thus limited by the SAR parameters. This paper explores these limits and proposes a generalized chirp-scaling approach for extending the utility of frequency-domain processing. We demonstrate how different order approximations of the SAR signal in the 2-D frequency domain affect image focusing for varying SAR parameters. From these results, a guideline is set forth, which suggests the required order of approximation terms for proper focusing. A proposed generalized frequency-domain processing approach is derived. This method is an efficient arbitrary-order CSA that processes the data using the appropriate number of approximation terms. The new method is demonstrated using simulated data.

Robust Projection Indices

Summary Loosely speaking a robust projection index is one that prefers projections involving true clusters over projections consisting of a cluster and an outlier. We introduce a mathematical definition of one-dimensional index robustness and describe a numerical experiment to measure it. We design five new indices based on measuring divergence from Student's t-distribution which are intended to be especially robust: the experiment shows that they are more robust than several established indices. The experiment also reveals more generally that the robustness of moment indices depends on the number of approximation terms, providing additional practical guidance for existing projection pursuit implementations. We investigate the theoretical properties of one new Student t-index and Hall's index and show that the new index automatically adapts its robustness to the degree of outlier contamination. We conclude by outlining the possibilities for extending our experiments to both higher dimensions and other new indices.