Detection Tests Using Sparse Models, With Application to Hyperspectral Data

Abstract

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.The tests are then applied to massive astrophysical hyperspectral data in the context of the European Southern Observatory's (ESO) Multi Unit Spectroscopic Explorer (MUSE) instrument. Experiments show that the introduced detection methods are more efficient than the GLR, confirming the pertinence of our approaches towards detection goals.

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

“…In [20][21][22], we introduced two detection tests based on MAP estimates, which were shown to be more powerful for sparse signals than classical methods, such as the unconstrained GLR test [19]. A connection was found with earlier works of Fan [23] and Basu [24], and with the Max test described in [5].…”

“…The tests of [20][21][22] were applied to 3D (hyperspectral) data and relied on a dedicated one-dimensional (1D) redundant spectral dictionary. As an illustration of the proposed method, we show here that one can improve on the results of [20][21][22] by using spatio-spectral dictionaries.…”

“…As an illustration of the proposed method, we show here that one can improve on the results of [20][21][22] by using spatio-spectral dictionaries. These dictionaries exploit both the sparsity of the data along the λ dimension and the information leakage caused by the 3D PSF over several voxels.…”

SELFI: an object-based, Bayesian method for faint emission line source detection in MUSE deep field data cubes

“…procedure that results from the matched filter and the max-test leads to the same results obtained by the constrained likelihood ratio approach developed by Paris et al (2013).…”

Tracking the Lyman alpha emission line in the CircumGalactic Medium in MUSE data

“…Since MUSE first light in January 2014, several studies (Paris et al, 2013), (Meillier et al, 2016) have already been conducted on MUSE data, with the aim to detect faint young galaxies. These latter are characterized by the presence a powerful Lyman-α emission line in their emission spectrum.…”