Improving SNR with a maximum likelihood compressed sensing decoder for multiplexed PET detectors

We present two novel contributions for multiplexing PET detectors. First, we develop a new theoretical framework for investigating multiplexing schemes for PET detectors using the theory of "compressed sensing" (CS). Second, we develop a new CS decoder that improves the multiplexing SNR. Because the photon events in PET are discrete, the detected photon signals are very sparse. CS theory can be used to specify multiplexing topologies that minimize the number of unique readout channels. In the case of readout for a PET detector array, CS can determine detector sampling criteria for effective "decoding" of the individual detector pixel signals and guide the design of multiplexing topologies for PET detector readouts. However, conventional CS methods do not account for the underlying noise model. Therefore, we develop a new method for decoding multiplexed detector signals that optimizes the SNR of the decoded detector pixel signals using maximum likelihood estimation, which we refer to as "maximum likelihood CS" (ML-CS) decoding. Using these results, we can describe any multiplexing readout scheme using a unified mathematical framework and formulate the optimal SNR estimator for recovering all detector signal information necessary to determine event interaction location, arrival time and energy with high precision. This ML-CS decoder can be applied to any multiplexing scheme such as standard Anger logic decoding. In this study, we study several different electronic multiplexing schemes for a given photodetector array design and use simulation studies to evaluate this new method. For example, for a conventional electronic multiplexing configuration known as "cross-strip multiplexing", we show that the ML-CS decoding algorithm can improve the SNR by 20-55% over conventional cross-strip readout decoding.