200 research outputs found
A Framework for Fast Image Deconvolution with Incomplete Observations
In image deconvolution problems, the diagonalization of the underlying
operators by means of the FFT usually yields very large speedups. When there
are incomplete observations (e.g., in the case of unknown boundaries), standard
deconvolution techniques normally involve non-diagonalizable operators,
resulting in rather slow methods, or, otherwise, use inexact convolution
models, resulting in the occurrence of artifacts in the enhanced images. In
this paper, we propose a new deconvolution framework for images with incomplete
observations that allows us to work with diagonalized convolution operators,
and therefore is very fast. We iteratively alternate the estimation of the
unknown pixels and of the deconvolved image, using, e.g., an FFT-based
deconvolution method. This framework is an efficient, high-quality alternative
to existing methods of dealing with the image boundaries, such as edge
tapering. It can be used with any fast deconvolution method. We give an example
in which a state-of-the-art method that assumes periodic boundary conditions is
extended, through the use of this framework, to unknown boundary conditions.
Furthermore, we propose a specific implementation of this framework, based on
the alternating direction method of multipliers (ADMM). We provide a proof of
convergence for the resulting algorithm, which can be seen as a "partial" ADMM,
in which not all variables are dualized. We report experimental comparisons
with other primal-dual methods, where the proposed one performed at the level
of the state of the art. Four different kinds of applications were tested in
the experiments: deconvolution, deconvolution with inpainting, superresolution,
and demosaicing, all with unknown boundaries.Comment: IEEE Trans. Image Process., to be published. 15 pages, 11 figures.
MATLAB code available at
https://github.com/alfaiate/DeconvolutionIncompleteOb
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
An inertial forward-backward algorithm for monotone inclusions
In this paper, we propose an inertial forward backward splitting algorithm to
compute a zero of the sum of two monotone operators, with one of the two
operators being co-coercive. The algorithm is inspired by the accelerated
gradient method of Nesterov, but can be applied to a much larger class of
problems including convex-concave saddle point problems and general monotone
inclusions. We prove convergence of the algorithm in a Hilbert space setting
and show that several recently proposed first-order methods can be obtained as
special cases of the general algorithm. Numerical results show that the
proposed algorithm converges faster than existing methods, while keeping the
computational cost of each iteration basically unchanged.Comment: The final publication is available at http://link.springer.co
On alternating direction methods for monotropic semidefinite programming
Ph.DDOCTOR OF PHILOSOPH
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