Simultaneous reconstruction of tissue attenuation and radioactivity maps in SPECT

The importance of accurate attenuation correction in single photon emission computed tomography (SPECT) has been widely recognized. In this paper, we propose a novel scheme of simultaneous reconstruction of the tissue attenuation map and the radioactivity distribution from SPECT emission sinograms, which is obviously beneficial when the transmission data is missing for cost or efficiency reasons. Our strategy combines the SPECT image formation and data measurement models, whereas the attenuation parameters are treated as random variables with known prior statistics. After converting the models to state space representation, the extended Kalman filtering procedures are adopted to linearize the equations and to provide the joint estimates in an approximate optimal sense. Experiments have been performed on synthetic data and real scanning data to illustrate abilities and benefits of the method.