Em Filter for Time-varying Spect Reconstruction

The new filtering algorithm EM (expectation maximization) filter is introduced and is validated numerically by applying it to solve the ill-posed inverse problem of reconstructing a time-varying medical image. A linear statespace stochastic approach based on a Markov process is utilized to model the problem, while no precise a-priori information about the underlying dynamics of the physical process is required. The method is tested for the case of image reconstruction from noisy data in dynamic single photon emission computed tomography (SPECT), where the signal strength changes substantially over the time required for the noisy data acquisition. Numerical results corroborate the effectiveness of the reconstruction method. AMS Subject Classification: 93E11, 93E10, 34K29, 49N45, 60G35, 62G05, 62M05, 68U10, 94A08, 90C25