4,842 research outputs found
A method for space-variant deblurring with application to adaptive optics imaging in astronomy
Images from adaptive optics systems are generally affected by significant
distortions of the point spread function (PSF) across the field of view,
depending on the position of natural and artificial guide stars. Image
reduction techniques circumventing or mitigating these effects are important
tools to take full advantage of the scientific information encoded in AO
images. The aim of this paper is to propose a method for the deblurring of the
astronomical image, given a set of samples of the space-variant PSF. The method
is based on a partitioning of the image domain into regions of isoplanatism and
on applying suitable deconvolution methods with boundary effects correction to
each region. The effectiveness of the boundary effects correction is proved.
Moreover, the criterion for extending the disjoint sections to partially
overlapping sections is validated. The method is applied to simulated images of
a stellar system characterized by a spatially variable PSF. We obtain good
photometric quality, and therefore good science quality, by performing aperture
photometry on the deblurred images. The proposed method is implemented in IDL
in the Software Package "Patch", which is available on
http://www.airyproject.eu.Comment: 11 pages, 9 figures, 7 tables, accepted by A&
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
Recent Progress in Image Deblurring
This paper comprehensively reviews the recent development of image
deblurring, including non-blind/blind, spatially invariant/variant deblurring
techniques. Indeed, these techniques share the same objective of inferring a
latent sharp image from one or several corresponding blurry images, while the
blind deblurring techniques are also required to derive an accurate blur
kernel. Considering the critical role of image restoration in modern imaging
systems to provide high-quality images under complex environments such as
motion, undesirable lighting conditions, and imperfect system components, image
deblurring has attracted growing attention in recent years. From the viewpoint
of how to handle the ill-posedness which is a crucial issue in deblurring
tasks, existing methods can be grouped into five categories: Bayesian inference
framework, variational methods, sparse representation-based methods,
homography-based modeling, and region-based methods. In spite of achieving a
certain level of development, image deblurring, especially the blind case, is
limited in its success by complex application conditions which make the blur
kernel hard to obtain and be spatially variant. We provide a holistic
understanding and deep insight into image deblurring in this review. An
analysis of the empirical evidence for representative methods, practical
issues, as well as a discussion of promising future directions are also
presented.Comment: 53 pages, 17 figure
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
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