Algebraic Approach to Phase Problem

Speaker: 
Pavel Trochtchanovitch
Event Date and Time: 
Thu, 2017-02-02 15:00 - 16:00
Location: 
Henn 309
Local Contact: 
Kirk Madison
Intended Audience: 
Graduate

In this talk we’ll discuss a “phase problem” – reconstruction of a signal from absolute value of its Fourier transform; with the only constraint being finite (though not known exactly) signal support.

With the help of “sampling theorem” it will be shown how this “phase problem” is equivalent to a system of non-linear equations; a fundamental difference between numerical solutions for 1D and 2D cases will be illustrated (why 1D case result in 2 to the power of ”number of points” solutions, and 2D case doesn’t?), and several numerical examples will be presented.

 

The theoretical part of this presentation is based on works done for my thesis in 2004, with several new improvements made recently.

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