Graph Signal Processing for Heterogeneous Change Detection Part II: Spectral Domain Analysis

This is the second part of the paper that provides a new strategy for the heterogeneous change detection (HCD) problem, that is, solving HCD from the perspective of graph signal processing (GSP). We construct a graph to represent the structure of each image, and treat each image as a graph signal defined on the graph. In this way, we can convert the HCD problem into a comparison of responses of signals on systems defined on the graphs. In the part I, the changes are measured by comparing the structure difference between the graphs from the vertex domain. In this part II, we analyze the GSP for HCD from the spectral domain. We first analyze the spectral properties of the different images on the same graph, and show that their spectra exhibit commonalities and dissimilarities. Specially, it is the change that leads to the dissimilarities of their spectra. Then, we propose a regression model for the HCD, which decomposes the source signal into the regressed signal and changed signal, and requires the regressed signal have the same spectral property as the target signal on the same graph. With the help of graph spectral analysis, the proposed regression model is flexible and scalable. Experiments conducted on seven real data sets show the effectiveness of the proposed method.