On-the-fly Approximation of Multivariate Total Variation Minimization

In the context of change-point detection, addressed by Total Variation minimization strategies, an efficient on-the-fly algorithm has been designed leading to exact solutions for univariate data. In this contribution, an extension of such an on-the-fly strategy to multivariate data is investigated. The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker conditions on the dual problem. Showing that the non-local nature of the multivariate setting precludes to obtain an exact on-the-fly solution, we devise an on-the-fly algorithm delivering an approximate solution, whose quality is controlled by a practitioner-tunable parameter, acting as a trade-off between quality and computational cost. Performance assessment shows that high quality solutions are obtained on-the-fly while benefiting of computational costs several orders of magnitude lower than standard iterative procedures. The proposed algorithm thus provides practitioners with an efficient multivariate change-point detection on-the-fly procedure

Online Graph-Based Change Point Detection in Multiband Image Sequences

The automatic detection of changes or anomalies between multispectral and hyperspectral images collected at different time instants is an active and challenging research topic. To effectively perform change-point detection in multitemporal images, it is important to devise techniques that are computationally efficient for processing large datasets, and that do not require knowledge about the nature of the changes. In this paper, we introduce a novel online framework for detecting changes in multitemporal remote sensing images. Acting on neighboring spectra as adjacent vertices in a graph, this algorithm focuses on anomalies concurrently activating groups of vertices corresponding to compact, well-connected and spectrally homogeneous image regions. It fully benefits from recent advances in graph signal processing to exploit the characteristics of the data that lie on irregular supports. Moreover, the graph is estimated directly from the images using superpixel decomposition algorithms. The learning algorithm is scalable in the sense that it is efficient and spatially distributed. Experiments illustrate the detection and localization performance of the method