Robust Control of Varying Weak Hyperspectral Target Detection With Sparse Nonnegative Representation

Abstract

Abstract-In this study, a multiple-comparison approach is developed for detecting faint hyperspectral sources. The detection method relies on a sparse and non-negative representation on a highly coherent dictionary to track a spatially varying source. A robust control of the detection errors is ensured by learning the test statistic distributions on the data. The resulting control is based on the false discovery rate, to take into account the large number of pixels to be tested. This method is applied to data recently recorded by the three-dimensional spectrograph Multi-Unit Spectrograph Explorer.

Global error control procedure for spatially structured targets

“…For a symmetrically distributed noise, these features are also symmetrical under H 0 and high positive values are expected for target pixels (see [7]). …”

“…COMET can be exploited in the framework of sparse nonnegative representation such as developed in [7]. Each feature is now defined as…”

“…In [7], a detection method for galactic halos in hyperspectral data produced by the MUSE instrument [8], [9] was developed. This method was based on BH procedure which did not take connectivity into account, whereas halos are expected to exhibit strong connectivity.…”

“…COMET elaborates on both a recent alternative class of FDR controlling procedures [5], [6] and a recent method [7] that yields robust control under weak assumptions on the noise. We propose a relevant framework in the context of multiple-testing problem where target exhibit connected structures.…”

“…Detection of galactic halo in hyperspectral data satisfies these assumptions. Using a simple and robust procedure [7], such feature statistics are built and motivated the method presented in this paper.…”