Multiple concentric annuli for characterizing spatially nonuniform backgrounds

A method is presented for estimating the background at a given location on a sky map by interpolating the estimated background from a set of concentric annuli which surround this location. If the background is nonuniform but smoothly varying, this method provides a more accurate (though less precise) estimate than can be obtained with a single annulus. Several applications of multi-annulus background estimation are discussed, including direct testing for point sources in the presence of a nonuniform background, the generation of "surrogate maps" for characterizing false alarm rates, and precise testing of the null hypothesis that the background is uniform.Comment: 35 pages, including 19 embedded postscript figures; LaTeX with AAS macros. Minor revisions, improved figures, as suggested by referee. To appear in Astrophysical Journa

Subpixel anomalous change detection in remote sensing imagery

Abstract—A machine-learning framework for anomalous change detection is extended to the situation in which the anomalous change is smaller than a pixel. Although the existing framework can be applied to (and does have power against) the subpixel case, it is possible to optimize that framework for the subpixel case when the size of the anomalous change is known. The limit of infintesimally small anomaly turns out to be welldefined, and provides a new parameter-free anomalous change detector which is effective over a range of subpixel anomalies, and continues to have reasonable power against the full-pixel case. I

Stochastic to deterministic crossover of fractal dimension for a Langevin equation

Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of deterministic chaos at longer time scales for data generated from a Langevin equation that has a strange attractor in the limit of zero noise. Our results suggest that the crossover occurs at such short time scales that there is little chance of finite-dimensional Brownian noise being incorrectly identified as deterministic chaos.Comment: 12 pages including 3 figures, RevTex and epsf. To appear Phys. Rev. E, April, 199