809 research outputs found
A simple but efficient algorithm for multiple-image deblurring
We consider the simultaneous deblurring of a set of noisy images whose point
spread functions are different but known and spatially invariant, and the noise
is Gaussian. Currently available iterative algorithms that are typically used
for this type of problem are computationally expensive, which makes their
application for very large images impractical. We present a simple extension of
a classical least-squares (LS) method where the multi-image deblurring is
efficiently reduced to a computationally efficient single-image deblurring. In
particular, we show that it is possible to remarkably improve the
ill-conditioning of the LS problem by means of stable operations on the
corresponding normal equations, which in turn speed up the convergence rate of
the iterative algorithms. The performance and limitations of the method are
analyzed through numerical simulations. Its connection with a column weighted
least-squares approach is also considered in an appendix.Comment: 9 pages, 16 figures. High resolution figures available upon demand.
To appear in A&
Scaled Gradient Projection Methods for Astronomical Imaging
This book is a collection of 19 articles which reflect the courses given at the CollĂšge de France/Summer school âReconstruction d'images â Applications astrophysiquesâ held in Nice and FrĂ©jus, France, from June 18 to 22, 2012. The articles presented in this volume address emerging concepts and methods that are useful in the complex process of improving our knowledge of the celestial objects, including Earth
Quantum limits of super-resolution in reconstruction of optical objects
We investigate analytically and numerically the role of quantum fluctuations
in reconstruction of optical objects from diffraction-limited images. Taking as
example of an input object two closely spaced Gaussian peaks we demonstrate
that one can improve the resolution in the reconstructed object over the
classical Rayleigh limit. We show that the ultimate quantum limit of resolution
in such reconstruction procedure is determined not by diffraction but by the
signal-to-noise ratio in the input object. We formulate a quantitative measure
of super-resolution in terms of the optical point-spread function of the
system.Comment: 23 pages, 7 figures. Submitted to Physical Review A e-mail:
[email protected]
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