Recently, the limited-angle TOF-PET system has become an active topic mainly due to the considerable reduction of hardware cost and potential applicability for performing needle biopsy on patients while in the scanner. However, this kind of measurement configurations oftentimes suffers from the deteriorated reconstructed images, because insufficient data are observed. The established theory of Compressed Sensing (CS) provides a potential framework for attacking this problem. CS claims that the imaged object can be faithfully recovered from highly underdetermined observations, provided that it can be sparse in some transformed domain.In here a first attempt was made in applying the CS framework to TOF-PET imaging for two undersampling configurations. First, to deal with undersampling TOF-PET imaging, an efficient sparsity-promoted algorithm was developed for combined regularizations of p-TV and l1-norm, where it was found that (a) it is capable of providing better reconstruction than the traditional EM algorithm, and (b) the 0.5-TV regularization was significantly superior to the regularizations of 0-TV and 1-TV, which are widely investigated in the open literature. Second, a general framework was proposed for sparsity-promoted ART, where accelerated techniques of multi-step and order-set were simultaneously used. From the results, it was observed that the accelerated sparsity-promoted ART method was capable of providing better reconstruction than traditional ART. Finally, a relationship was established between the number of detectors (or the range of angle) and TOF time resolution, which provided an empirical guidance for designing novel low-cost TOF-PET systems while ensuring good reconstruction quality.
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