Compressed sensing (CS) estimation approaches rely on a priori sparsity to significantly reduce the number of samples needed to provide high sampling fidelity, relative to the normal Shannon-Nyquist limit. Accordingly, CS approaches are of considerable interest for detector multiplexing in applications which have inherently sparse signals (e.g., the two correlated photon detection events in PET imaging). However, CS approaches also tend to fare poorly in the presence of noise, which has limited their applicability in practice. In this work, we show that CS estimation can be used to provide an estimate of the support of an image. This estimated support is then used as a constraint for maximum likelihood image reconstruction. This approach has robust noise performance and provides high reconstruction fidelity.
