  Anomalous change detection (ACD) is an important problem in remote sensing
image processing. Detecting not only pervasive but also anomalous or extreme
changes has many applications for which methodologies are available. This paper
introduces a nonlinear extension of a full family of anomalous change
detectors. In particular, we focus on algorithms that utilize Gaussian and
elliptically contoured (EC) distribution and extend them to their nonlinear
counterparts based on the theory of reproducing kernels' Hilbert space. We
illustrate the performance of the kernel methods introduced in both pervasive
and ACD problems with real and simulated changes in multispectral and
hyperspectral imagery with different resolutions (AVIRIS, Sentinel-2,
WorldView-2, and Quickbird). A wide range of situations is studied in real
examples, including droughts, wildfires, and urbanization. Excellent
performance in terms of detection accuracy compared to linear formulations is
achieved, resulting in improved detection accuracy and reduced false-alarm
rates. Results also reveal that the EC assumption may be still valid in Hilbert
spaces. We provide an implementation of the algorithms as well as a database of
natural anomalous changes in real scenarios http://isp.uv.es/kacd.html.
