Error control for the detection of rare and weak signatures in massive data

In this paper, we address the general issue of detecting rare and weak signatures in very noisy data. Multiple hypothe ses testing approaches can be used to extract a list of com ponents of the data that are likely to be contaminated by a source while controlling a global error criterion. However most of efficients methods available in the literature are de rived for independent tests. Based on the work of Benjamini and Yekutieli [1], we show that under some classical positivity assumptions, the Benjamini-Hochberg procedure for False Discovery Rate (FDR) control can be directly applied to the result produced by a very common tool in signal and image processing: the matched filter. This shows that despite the de pendency structure between the components of the matched filter output, the Benjamini-Hochberg procedure still guaran tee the FDR control. This is illustrated on both synthetic and real data.