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|標題:||Coded aperture ptychography: uniqueness and reconstruction||作者:||Pengwen Chen
|關鍵字:||ptychography;phase retrieval;uniqueness;geometric convergence;twin-image ambiguity||出版社:||Inverse Problems||Project:||Inverse Problems||摘要:||
Uniqueness of solution is proved for any ptychographic scheme with a random
mask under a minimum overlap condition and local geometric convergence
analysis is given for the alternating projection (AP) and Douglas–Rachford
(DR) algorithms. DR is shown to possess a unique fixed point in the object
domain and for AP a simple criterion for distinguishing the true solution
among possibly many fixed points is given.
A minimalist scheme, where the adjacent masks overlap 50% of the area
and each pixel of the object is illuminated by exactly four illuminations, is
conveniently parametrized by the number q of shifted masks in each direction.
The lower bound 1 − (C/q)^2
is proved for the geometric convergence rate of
the minimalist scheme, predicting a poor performance with large q which is
confirmed by numerical experiments. The twin-image ambiguity is shown to
arise for certain Fresnel masks and degrade the performance of reconstruction.
Extensive numerical experiments are performed to explore the general
features of a well-performing mask, the optimal value of q and the robustness
with respect to measurement noise.
|Appears in Collections:||應用數學系所|
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