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Isao Yamada, Tokyo Inst. of
|Friday, September 13, 2013, 10 a.m., room HFT
recovery of a smooth phase surface from its wrapped samples, the
so-called two-dimensional phase unwrapping, has been a key for
estimating crucial physical information such as the surface topography
as measured by interferometric synthetic aperture radar (InSAR) or
interferometric synthetic aperture sonar (InSAS), the degree of
magnetic field inhomogeneity in the water/fat separation problem in
magnetic resonance imaging (MRI), and the accurate profile of
mechanical parts by x-ray.
Although the two-dimensional phase unwrapping can seriously influence the accuracy of the estimated physical information, a technically reliable phase unwrapping technique has been a longstanding missing puzzle piece. Indeed, almost all algorithms are suffering from the path dependence of the estimated unwrapped phase mainly because they do not care about the smoothness of the unwrapped phase surface over the continuous domain but just try to estimate the unwrapped phase at finite samples as a solution of a certain NP-Hard problem.
In this talk, we present, in the spirit of functional data analysis, a completely different algebraic approach to the two-dimensional phase unwrapping problem. The proposed approach is designed by combining the ideas in the algebraic phase unwrapping developed originally by the speaker with techniques for piecewise polynomial interpolation of two-dimensional data sequences. Remarkably, the proposed approach can guarantee the path independence of the estimated unwrapped phase under certain conditions.
Isao Yamada is a Professor with the Department of Communications and Computer Engineering, Tokyo Institute of Technology. His current research interests are in mathematical signal processing, nonlinear inverse problems, and optimization theory. He has been an associate editor for many journals, e.g., the IEEE Trans. Signal Processing (2008-2011). He is now serving as the Editor-in-Chief of the IEICE Trans. Fundamentals, and as an editorial board member of the Numerical Functional Analysis and Optimization (Taylor and Francis) and the Multidimensional Systems and Signal Processing (Springer). Currently, he is also serving as a member of the IEEE Signal Processing Theory and Methods Technical Committee. He received the IEICE Achievement Award in 2009, the ICF Research Award in 2004, the Docomo Mobile Science Award (Fundamental Science Division) in 2005 and the Fujino Prize in 2008