Successful performance of radiological search mission is dependent on effective utilization of mixture of signals. Examples of modalities include, e.g., EO imagery and gamma radiation data, or radiation data collected during multiple events. In addition, elevation data or spatial proximity can be used to enhance the performance of acquisition systems. State of the art techniques in processing and exploitation of complex information manifolds rely on diffusion operators. Our approach involves machine learning techniques based on analysis of joint data- dependent graphs and their associated diffusion kernels. Then, the significant eigenvectors of the derived fused graph Laplace and Schroedinger operators form the new representation, which provides integrated features from the heterogeneous input data. The families of data-dependent Laplace and Schroedinger operators on joint data graphs, shall be integrated by means of appropriately designed fusion metrics. These fused representations are used for target and anomaly detection.
We shall introduce a novel methodology for data reconstruction and recovery, based on composite wavelet
representations. These representations include shearlets and crystallographic wavelets, among others, and they
allow for an increased directional sensitivity in comparison with the standard multiscale techniques. Our new
approach allows us to recover missing data, due to sparsity of composite wavelet representations, especially when
compared to inpainting algorithms induced by traditional wavelet representations, and also due to the
flexibility of our variational approach.