Improved compressed sensing multiplexing for PET detector readout

We have developed new multiplexing method based on compressed sensing (CS) for PET detector readouts. Unlike presently known multiplexing methods, this new scheme can accurately measure the energy and position of pile up events while improving the signal-to-noise ratio of the detector. We introduce a new method for constructing sensing matrices with superior performance over commonly used "random construction" CS methods. Using a maximum-likelihood decoder that we have previously developed, we show through simulations that the new multiplexing method can position intercrystal scatter events and pile up with nearly 100% accuracy. Further, the new multiplexing method yields a 40-1260% improvement in SNR compared to cross-strip multiplexing at a 4-to-1 multiplexing ratio.