I have a 2-D signal collected in the frequency vs time domain. There is a feature of interest in this signal (a chirp) appearing at some arbitrary times which I have successfully extracted using a properly orientated 2-D Gabor filter.
What I would like to do is exploit the detection of this feature to represent the data in a sparse domain, so that Compressed Sensing can be used to capture the data regions which contain the chirp trait without sampling the entire data set a-la Nyquist.
I have searched for a way to do this online but haven't found very much. The literature I've read says that the basis must be orthogonal for perfect reconstruction, and that Gabor domain is most times not, but given that I'm only interested in a faster detection (yes contains/no, does not contain chirp) and not really a perfect reconstruction, is such a thing possible? If the approach above is not the best way to go about doing this, recommendations would be welcome as well.