336 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 convergent blind deconvolution method for post-adaptive-optics astronomical imaging
In this paper we propose a blind deconvolution method which applies to data
perturbed by Poisson noise. The objective function is a generalized
Kullback-Leibler divergence, depending on both the unknown object and unknown
point spread function (PSF), without the addition of regularization terms;
constrained minimization, with suitable convex constraints on both unknowns, is
considered. The problem is nonconvex and we propose to solve it by means of an
inexact alternating minimization method, whose global convergence to stationary
points of the objective function has been recently proved in a general setting.
The method is iterative and each iteration, also called outer iteration,
consists of alternating an update of the object and the PSF by means of fixed
numbers of iterations, also called inner iterations, of the scaled gradient
projection (SGP) method. The use of SGP has two advantages: first, it allows to
prove global convergence of the blind method; secondly, it allows the
introduction of different constraints on the object and the PSF. The specific
constraint on the PSF, besides non-negativity and normalization, is an upper
bound derived from the so-called Strehl ratio, which is the ratio between the
peak value of an aberrated versus a perfect wavefront. Therefore a typical
application is the imaging of modern telescopes equipped with adaptive optics
systems for partial correction of the aberrations due to atmospheric
turbulence. In the paper we describe the algorithm and we recall the results
leading to its convergence. Moreover we illustrate its effectiveness by means
of numerical experiments whose results indicate that the method, pushed to
convergence, is very promising in the reconstruction of non-dense stellar
clusters. The case of more complex astronomical targets is also considered, but
in this case regularization by early stopping of the outer iterations is
required
Regularized Gradient Descent: A Nonconvex Recipe for Fast Joint Blind Deconvolution and Demixing
We study the question of extracting a sequence of functions
from observing only the sum of
their convolutions, i.e., from . While convex optimization techniques
are able to solve this joint blind deconvolution-demixing problem provably and
robustly under certain conditions, for medium-size or large-size problems we
need computationally faster methods without sacrificing the benefits of
mathematical rigor that come with convex methods. In this paper, we present a
non-convex algorithm which guarantees exact recovery under conditions that are
competitive with convex optimization methods, with the additional advantage of
being computationally much more efficient. Our two-step algorithm converges to
the global minimum linearly and is also robust in the presence of additive
noise. While the derived performance bounds are suboptimal in terms of the
information-theoretic limit, numerical simulations show remarkable performance
even if the number of measurements is close to the number of degrees of
freedom. We discuss an application of the proposed framework in wireless
communications in connection with the Internet-of-Things.Comment: Accepted to Information and Inference: a Journal of the IM
A new semi-blind deconvolution approach for Fourier-based image restoration: an application in astronomy
The aim of this paper is to develop a new optimization algorithm for the restoration of an image starting from samples of its Fourier Transform, when only partial information about the data frequencies is provided. The corresponding constrained optimization problem is approached with a cyclic block alternating scheme, in which projected gradient methods are used to find a regularized solution. Our algorithm is then applied to the imaging of high-energy radiation emitted during a solar flare through the analysis of the photon counts collected by the NASA RHESSI satellite. Numerical experiments on simulated data show that, both in presence and in absence of statistical noise, the proposed approach provides some improvements in the reconstructions
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