Mathematics, Systems and Robotics Seminar 

03/12/2004, 15:00 — 16:00 — Conference Room, Instituto de Sistemas e Robótica, North Tower, 7th floor, IST
José Bioucas Dias, N/A

Absolute Phase Estimation

Phase estimation is the process of recovering the phase (the so-called absolute phase) from noisy and modulo $2\pi$ (the so-called wrapped phase) observations. The need for determining absolute phase is common to many classes of signal/image applications. For example, interferometric synthetic aperture radar uses two or more antennas to measure the phase difference between the antennas and the terrain; the topography is then inferred from the difference between those phases. In magnetic resonance imaging, phase is used to measure flow and temperature temperature, to visualize veins in the tissue (venography), to map the principal magnetic field, which is the basis for several correction techniques, and to separate water and fat. In optical interferometry, phase measurements are used to detect objects shape, deformation, and vibration. In this talk I introduce the absolute phase estimation problem and present a Bayesian approach aimed at to the computation of the "maximum a posteriori estimate" (MAP). The heaviest step in computing the MAP estimate is an integer optimization problem of an $L^p$ type norm. For $p\ge 1$, we solve this optimization in polinomial time by mapping the initial problem onto a series of graph-cuts on given graph. For $p\ge 1$, the proposed method also solves any of the so-called "minimum $L^p$" approaches to phase unwrapping (i.e., absolute phase estimation without noise), to which solutions were know only for $p=1$. A set of experimental results illustrates the effectiveness of the proposed approach.