Constrained likelihood ratios for detecting sparse signals in highly noisy 3D data

We propose a method aimed at detecting weak, sparse signals in highly noisy three-dimensional (3D) data. 3D data sets usually combine two spatial directions x and y (e.g. image or video frame dimensions) with an additional direction λ (e.g. temporal, spectral or energy dimension). Such data most often suffer from information leakage caused by the acquisition system´s point spread functions, which may be different and variable in the three dimensions. The proposed test is based on dedicated 3D dictionaries, and exploits both the sparsity of the data along the λ direction and the information spread in the three dimensions. Numerical results are shown in the context of astrophysical hyperspectral data, for which the proposed 3D model substantially improves over 1D detection approaches.