Detection Tests Using Sparse Models, With Application to Hyperspectral Data

The problem of finding efficient methods for the detection of unknown sparse signals buried in noise is addressed. We present two detection tests adapted to sparse signals, based on the maximum a posteriori (MAP) estimate of the sparse vector of parameters. The first is the posterior density ratio test, which computes the ratio of the a posteriori distribution under each hypothesis of the data model. The second is a likelihood ratio test in which the MAP replaces the maximum likelihood (ML) estimate. The behaviors and the relative differences between these tests are investigated through a detailed study of their structural characteristics. The proposed approaches are compared to the generalized likelihood ratio test (GLR), showing successful results in the case of a simple model first and then for a model in which sparsity is promoted through the use of a highly redundant dictionary.