A theoretical Gaussian framework for anomalous change detection in hyperspectral images

Exploitation of temporal series of hyperspectral images is a relatively new discipline that has a wide variety of possible applications in fields like remote sensing, area surveillance, defense and security, search and rescue and so on. In this work, we discuss how images taken at two different times can be processed to detect changes caused by insertion, deletion or displacement of small objects in the monitored scene. This problem is known in the literature as anomalous change detection (ACD) and it can be viewed as the extension, to the multitemporal case, of the well-known anomaly detection problem in a single image. In fact, in both cases, the hyperspectral images are processed blindly in an unsupervised manner and without a-priori knowledge about the target spectrum. We introduce the ACD problem using an approach based on the statistical decision theory and we derive a common framework including different ACD approaches. Particularly, we clearly define the observation space, the data statistical distribution conditioned to the two competing hypotheses and the procedure followed to come with the solution. The proposed overview places emphasis on techniques based on the multivariate Gaussian model that allows a formal presentation of the ACD problem and the rigorous derivation of the possible solutions in a way that is both mathematically more tractable and easier to interpret. We also discuss practical problems related to the application of the detectors in the real world and present affordable solutions. Namely, we describe the ACD processing chain including the strategies that are commonly adopted to compensate pervasive radiometric changes, caused by the different illumination/atmospheric conditions, and to mitigate the residual geometric image co-registration errors. Results obtained on real freely available data are discussed in order to test and compare the methods within the proposed general framework.