Generalized likelihood ratio test change detection with optical theorem constraint

We demonstrate a new application of the optical theorem to enhance the detection, from noisy scattering data, of an unknown scatterer embedded in an unknown background medium. The proposed methodology is based on a generalized likelihood ratio test detector with an additional constraint that must be obeyed by the scattered field data if the scatterer is known to be passive, lossless, or active. The constraint in question is based on the classical optical theorem, which is used throughout this paper in its most general form applicable to arbitrary probing fields and background media. It relies on background field information, which is accessible in many practical applications. This also reveals, from a fundamental wave physics point of view, that background information is highly relevant in extra ways beyond the basic background suppression operation. This "optical theorem constraint" is discussed in a general Hilbert space framework that applies to a broad class of scattering systems. Particular forms of the optical theorem constraint are presented for special cases, including spherical and cylindrical scanning systems for which it can be compactly expressed in the fundamental multipole representation. The pertinent change detection theory incorporating, via standard nonlinear programming, the physics-based optical theorem constraint is elaborated upon in detail, and the successful detection performance of this new change detection method is illustrated with examples.