Joe Qranfal, Charles Byrne
Department of Mathematics
Simon Fraser University
British Columbia, CANADA
Department of Mathematical Sciences
University of Massachusetts at Lowell
Lowellm, USA

Abstract. 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 state-space 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.

Received: May 31, 2011

AMS Subject Classification: 93E11, 93E10, 34K29, 49N45, 60G35, 62G05, 62M05, 68U10, 94A08, 90C25

Key Words and Phrases: estimation, stochastic filtering, Kalman filter, optimal filtering, state estimator, convex optimization, medical image, dynamic SPECT, cross-entropy, nonnegative reconstruction, hidden Markov model, expectation maximization, maximum likelihood, temporal regularization

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