Non-Bayesian Detection and Detectability of Anomalies From a Few Noisy Tomographic Projections

Abstract

The detection of an anomaly from a few noisy tomographic projections is addressed from the statistical point of view. An unknown scene is composed of a background, considered as a deterministic nuisance parameter, with a possibly hidden anomaly. Because the full pixel-by-pixel reconstruction is impossible, a parametric non-Bayesian approach is proposed to fill up the gap in the missing data. An optimal statistical test which eliminates the background and detects the anomaly is designed. The potential advantage of such an approach is its capacity to detect an anomaly/target hidden in background designed by an adversary to mask the anomaly. A key issue in the non-Bayesian anomaly detection, i.e., the problem of anomaly detectability, is stated and solved in this paper. In the case of a bivariate polynomial background defined on an unknown rectangular support, the size of detectable anomaly reaches its maximum defined by the number of elementary cells of X-ray detector and degree of the polynomial function