Optimization-based reconstruction with an image-total-variation constraint in PET

In an emission imaging method, emission imaging data are acquired for a subject using an emission imaging scanner (10) including radiation detectors (12). The emission imaging data are reconstructed to generate a reconstructed image by executing a constrained optimization program including a measure of data fidelity between the acquired emission imaging data an a reconstruct-image transformed by a data model of the imaging scanner to emission imaging data. During the reconstructing, each iteration of the constrained optimization program is constrained by an image variability constraint. The reconstructed image is displayed the reconstructed image on a display device. The emission imaging may be positron emission tomography (PET) imaging data, optionally acquired using a sparse detector array. The image variability constraint may be a constraint that an image total variation (image TV) of a latent image defined using a Gaussian blurring matrix be less than a maximum value.