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We review several detection strategies that account for the possible sparsity of target sources in data cubes. The considered sparsity can exist in the data acquisition space, or in some transform domain. Theoretical aspects of the detection tests are first described. Emphasis is then put on practical issues that may arise in hyperspectral data, such as spatio-spectral dependencies or very low Signal-to-Noise...
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...
We consider the problem of detecting a target signature which is known (up to an amplitude factor) to belong to a (possibly very) large library of signatures. Thus we know how each signature to be detected looks like, but we do not know which one is activated under H1. We propose a minimax approach for this problem aimed at maximizing the worst detection performance. Optimization issues and connections...
In an estimation framework, the suspected sparsity of an unknown vector of deterministic parameters is classically accounted for through thresholding functions, some of which being related to Maximum A Posteriori estimates with specific priors. In a detection framework, statistical tests applied to sparse vectors are classically designed so as to limit the focus of the test to a few active components,...
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