14,919 research outputs found
A weakly convergent fully inexact Douglas-Rachford method with relative error tolerance
Douglas-Rachford method is a splitting algorithm for finding a zero of the
sum of two maximal monotone operators. Each of its iterations requires the
sequential solution of two proximal subproblems. The aim of this work is to
present a fully inexact version of Douglas-Rachford method wherein both
proximal subproblems are solved approximately within a relative error
tolerance. We also present a semi-inexact variant in which the first subproblem
is solved exactly and the second one inexactly. We prove that both methods
generate sequences weakly convergent to the solution of the underlying
inclusion problem, if any
Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers
Ptychography has risen as a reference X-ray imaging technique: it achieves
resolutions of one billionth of a meter, macroscopic field of view, or the
capability to retrieve chemical or magnetic contrast, among other features. A
ptychographyic reconstruction is normally formulated as a blind phase retrieval
problem, where both the image (sample) and the probe (illumination) have to be
recovered from phaseless measured data. In this article we address a nonlinear
least squares model for the blind ptychography problem with constraints on the
image and the probe by maximum likelihood estimation of the Poisson noise
model. We formulate a variant model that incorporates the information of
phaseless measurements of the probe to eliminate possible artifacts. Next, we
propose a generalized alternating direction method of multipliers designed for
the proposed nonconvex models with convergence guarantee under mild conditions,
where their subproblems can be solved by fast element-wise operations.
Numerically, the proposed algorithm outperforms state-of-the-art algorithms in
both speed and image quality.Comment: 23 page
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