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Nuclear medicine imaging detectors are commonly multiplexed to reduce the number of readout channels. Because the underlying detector signals have a sparse representation, sparse recovery methods such as compressed sensing may be used to develop new multiplexing schemes. Random methods may be used to create sensing matrices that satisfy the restricted isometry property. However, the restricted isometry property provides little guidance for developing multiplexing networks with good signal-to-noise recovery capability. In this work, we describe compressed sensing using a maximum likelihood framework and develop a new method for constructing multiplexing (sensing) matrices that can recover signals more accurately in a mean square error sense compared to sensing matrices constructed by random construction methods. Signals can then be recovered by maximum likelihood estimation constrained to the support recovered by either greedy ℓ0 iterative algorithms or ℓ1-norm minimization techniques. We show that this new method for constructing and decoding sensing matrices recovers signals with 4%-110% higher SNR than random Gaussian sensing matrices, up to 100% higher SNR than partial DCT sensing matrices 50%-2400% higher SNR than cross-strip multiplexing, and 22%-210% higher SNR than Anger multiplexing for photoelectric events.