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Absolute phase image reconstruction: a stochastic nonlinear filtering approach

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2 Author(s)
J. M. N. Leitao ; Dept. de Engenharia Electrotecnica e de Comput., Inst. Superior Tecnico, Lisbon, Portugal ; M. A. T. Figueiredo

This paper formulates and proposes solutions to the problem of estimating/reconstructing the absolute (not simply modulo-2π) phase of a complex random field from noisy observations of its real and imaginary parts. This problem is representative of a class of important imaging techniques such as interferometric synthetic aperture radar, optical interferometry, magnetic resonance imaging, and diffraction tomography. We follow a Bayesian approach; then, not only a probabilistic model of the observation mechanism, but also prior knowledge concerning the (phase) image to be reconstructed, are needed. We take as prior a nonsymmetrical half plane autoregressive (NSHP AR) Gauss-Markov random field (GMRF). Based on a reduced order state-space formulation of the (linear) NSHP AR model and on the (nonlinear) observation mechanism, a recursive stochastic nonlinear filter is derived, The corresponding estimates are compared with those obtained by the extended Kalman-Bucy filter, a classical linearizing approach to the same problem. A set of examples illustrate the effectiveness of the proposed approach

Published in:

IEEE Transactions on Image Processing  (Volume:7 ,  Issue: 6 )