Abstract: A method processes a signal represented as a graph by first determining a graph spectral transform based on the graph. In a spectral domain, parameters of a graph filter are estimated using a training data set of unenhanced and corresponding enhanced signals. The graph filter is derived based on the graph spectral transform and the estimated graph filter parameters. Then, the signal is processed using the graph filter to produce an output signal. The processing can enhance signals such as images b denoising or interpolating missing samples.

Abstract: Targets are detected in a scene behind a wall by first transmitting a pulse through the wall. Then, a primary impulse response is detected by a sparse regularized least squares inversion applied to received signals corresponding to the reflected pulse. A delay operator that matches the primary impulse response to similar impulse responses in the received signals is also determined. A distortion of the pulse after the pulse passes through the wall but before the pulse is reflected by the target can also be determined. The distortion is used in an iterative process to refine the detection of the target and to suppress ghosting artifacts.