## Multi-source Absolute Phase Estimation: A Multi-precision Approach Based on Graph Cuts

#### Jose DiasInstituto Superior Tecnico

Absolute phase estimation is the nonlinear inverse problem of inferring phase from noisy modulo-$2\pi$ observations.
This problem plays a crucial role in a variety of holographic imaging systems, such as interferometric synthetic aperture radar, magnetic resonance imaging, and diffraction tomography. In all these modalities, the absolute phase carries information on the physical and geometrical properties of the objects under study such as shape, deformation, movement and surface's structure.

The noisy and periodic observation mechanism and the presence
discontinuities in the underlying true phase make absolute phase
estimation a hard inverse problem. A recent trend aimed at better
phase inferences is to use diversity (frequency, spatial, temporal,
etc.) in the acquisition process.

In this talk, we will present a discontinuity preserving Bayesian approach to absolute phase estimation from multi-source observations.
We assume a first order Markov random field (MRF) prior and a maximum {\em a posteriori} probability optimization viewpoint. The main road map is to first apply phase unwrapping ({\em i.e.}, eliminate the $2\pi$-periodic ambiguity) and then apply denoising. The involved discrete optimization problems are solved in a coarse-to-fine multi-precision fashion. In each precision, the underlying
optimization is mapped on a sequence of binary optimizations, which
we tackle by computing flows on appropriate graphs. To preserve
discontinuities, the potentials used in the MRF contain super-modular pairwise terms. This means that each of the binary optimization problems is difficult, if not impossible, to solve exactly. To attain good" approximation of the minimizers, we employ quadratic pseudo boolean optimizations -QPBO- and some extensions in each binary step.
Experimentally, the proposed approach gives state-of-the-art performance, both in terms of the estimated phase and the computational burden.

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