421 research outputs found
Non-parametric PSF estimation from celestial transit solar images using blind deconvolution
Context: Characterization of instrumental effects in astronomical imaging is
important in order to extract accurate physical information from the
observations. The measured image in a real optical instrument is usually
represented by the convolution of an ideal image with a Point Spread Function
(PSF). Additionally, the image acquisition process is also contaminated by
other sources of noise (read-out, photon-counting). The problem of estimating
both the PSF and a denoised image is called blind deconvolution and is
ill-posed.
Aims: We propose a blind deconvolution scheme that relies on image
regularization. Contrarily to most methods presented in the literature, our
method does not assume a parametric model of the PSF and can thus be applied to
any telescope.
Methods: Our scheme uses a wavelet analysis prior model on the image and weak
assumptions on the PSF. We use observations from a celestial transit, where the
occulting body can be assumed to be a black disk. These constraints allow us to
retain meaningful solutions for the filter and the image, eliminating trivial,
translated and interchanged solutions. Under an additive Gaussian noise
assumption, they also enforce noise canceling and avoid reconstruction
artifacts by promoting the whiteness of the residual between the blurred
observations and the cleaned data.
Results: Our method is applied to synthetic and experimental data. The PSF is
estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for
SDO/AIA using the 2012 Venus transit. Results show that the proposed
non-parametric blind deconvolution method is able to estimate the core of the
PSF with a similar quality to parametric methods proposed in the literature. We
also show that, if these parametric estimations are incorporated in the
acquisition model, the resulting PSF outperforms both the parametric and
non-parametric methods.Comment: 31 pages, 47 figure
A hybrid alternating proximal method for blind video restoration
International audienceOld analog television sequences suffer from a number of degradations. Some of them can be modeled through convolution with a kernel and an additive noise term. In this work, we propose a new blind deconvolution algorithm for the restoration of such sequences based on a variational formulation of the problem. Our method accounts for motion between frames, while enforcing some level of temporal continuity through the use of a novel penalty function involving optical flow operators, in addition to an edge-preserving regularization. The optimization process is performed by a proximal alternating minimization scheme benefiting from theoretical convergence guarantees. Simulation results on synthetic and real video sequences confirm the effectiveness of our method
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
- …