Detection and estimation of multiple weak signals in non-Gaussian noise

We address the problem of efficient detection and estimation of multiple weak signals in severe noise. To address this problem, we propose a concentrated peak representation (CPR) in which the spectral energy is concentrated in spectral peaks, and only the magnitudes and locations of the peaks are retained. We base our process on the cross spectral representation we have previously applied to other problems. The advantage of this representation is that it preserves the energy in signal components while significantly reducing the data volume. We demonstrate the method on a composite signal consisting of one billion samples, reducing the data volume by a factor of 1000 or more, and we demonstrate the detection of weak signals in the reduced representation.