Phase retrieval from multiple noisy observations
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2023-01-27 13:38
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KATKOVNIK, Vladimir. Phase retrieval from multiple noisy observations. In: Materials Science and Condensed Matter Physics, Ed. 8-th Edition, 12-16 septembrie 2016, Chişinău. Chişinău: Institutul de Fizică Aplicată, 2016, Editia 8, p. 367. ISBN 978-9975-9787-1-2.
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Materials Science and Condensed Matter Physics
Editia 8, 2016
Conferința "International Conference on Materials Science and Condensed Matter Physics"
8-th Edition, Chişinău, Moldova, 12-16 septembrie 2016

Phase retrieval from multiple noisy observations


Pag. 367-367

Katkovnik Vladimir
 
Tampere University of Technology
 
Disponibil în IBN: 7 august 2019


Rezumat

The phase retrieval problem is formulated as finding a complex-valued object x from real-valued intensity observations:  ys=|As x|2,   s = 1,2,…, L. (1) Design of the image formation operators As in (1) is a crucial moment in order to gain an observation diversity sufficient for reliable reconstruction of both object phase as well as object amplitude. Experiments for a set of distances ds (displaced sensor planes) is a common instrument to get the sufficient observations.  A phase modulation of the wavefront near the object plane is another popular tool to get diverse observations. In this case the phase modulation at the object plane plus the Fraunhofer wavefront propagation result in the observation model known as a coded diffraction pattern: ys=|FDs x|2,  s = 1,2,…, L, (2) where F denotes the Fourier transform and Ds stands for a phase mask formalized in (2) as a diagonal matrix of random complex exponents. This random phase modulation changes the spectrum of Fx in a radical way extending a distribution of the intensity from low to high frequency components. The measurement process in optics amounts to count the photons hitting the sensor’s elements what is well modeled by Poisson random variables.  A variational approach to wavefront reconstruction from multiple noisy Poissonian intensity observations is developed. Sparse modeling of amplitude and absolute phase of the object is one of the key elements of the derived algorithm enabling high-accuracy imaging from noisy intensity observations. Details of the developed algorithm as well as MATLAB demo-codes can be found in [1]. Here we show the results obtained by three different algorithms: the recent Truncated Wirtinger Flow (TWF) algorithm, which can be treated as the state-of-the-art in the field, our version of the Gerchberg-Saxton (GS) algorithm and the proposed SPAR algorithms. We show the results for the very nosy data: TWF is failed, SPAR gives the best clear results which are much better that those obtained by the GS algorithm.