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Blind deconvolution with an application to speckle imaging.

Law, BNF 1996 , 'Blind deconvolution with an application to speckle imaging.', PhD thesis, University of Tasmania.

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It is well known that the quality of an image that can be obtained from a groundbased
telescope is limited by the wavefront distortion associated with the atmospheric
turbulence. The turbulence is present as a result of the mixing of the warm and the cold
air. Although the turbulence affects both the amplitude and the phase of the wavefront,
the random phase aberration is found to be more important in the distortion of an image
than the magnitude distortion. As a result, the available light spread over a wide area
and the observed image is blurred.
This effect has hindered astronomers since the invention of the telescope in the 17t h
century. In order to reduce the effect of the atmospheric turbulence and improve the
quality of the image obtained at the ground-based telescopes, large collection aperture
telescopes have been built at high altitude places. Although the light gathering properties
of these modern telescopes are remarkable, the problem that originated from the
atmospheric turbulence has not been solved completely.
The aim of this study is to find ways that can compensate the effects of atmospheric
turbulence and provide a good quality image. There are two approaches proposed to
deal with this problem, namely the adaptive optics and the post-detection processing
approaches. The first half of the thesis is concerned with an adaptive optics approach
while the second half is concerned with a post-detection processing approach.
The adaptive optics approach compensates the wavefront distortion in real time. It uses
hardware designed to physically alter the optical path length of the distorted wavefront.
Thus a disturbance which is in the optical path just opposite to the disturbance associated
with the atmospheric turbulence is introduced so that both disturbances cancel.
Therefore, an accurate estimation of the disturbance introduced by the atmospheric turbulence is crucial in this approach. While the problem can be reformulated as a
standard least square problem from the measurements from Shack Hartmann sensor,
the least square problem is itself under-determined. This means that the quality of
distortion is limited by the number of measurements available, which in turn is limited
by the available light.
In order to solve this under-determined problem, a priori information needs to be applied
so as to put more constraints into the estimation. One piece of a priori information
that can be obtained is the statistics of the turbulence. This can be derived theoretically
using the Kolmogorov turbulence model. By incorporating this information into
the estimation, the problem becomes well-posed. As the simulation results show, the
accuracy in estimating the distorted wavefront is improved by incorporating the a priori
The second approach to compensate the disturbance is the post-detection processing
approach. This is founded upon the insight that short exposure images preserve frequencies
up to the diffraction limit. A variety of techniques have been proposed to
recover this diffraction-limited information, for example, the correlation-based techniques
of Knox-Thompson and bispectrum approaches. However, these techniques are
required to average the effects of atmospheric turbulence before the algorithm can be
applied to recover the object of interest.
Another approach is to consider the problem as a deconvolution problem in which the
object of interest is reconstructed based on the disturbance information and the short
exposure image. In this case the disturbance is unknown. It is a blind deconvolution
problem, that means we need to reconstruct the object from the short exposure image
without a statistical ensemble of distorted images. Three methods are discussed and
compared, they are the conjugate gradient approach, the projection-based approach
and the maximum likelihood approach. All these three methods can be formulated
using the Bayes' theorem but with different assumptions made on the noise statistics
and with different application of the a priori knowledge. They are compared in terms
of the convergence rate, the quality of the reconstructed image and also in the presence
of different noise levels.
As simulation results show, all these three algorithms can blindly deconvolve a blurred
image. In general, the projection-based algorithm and the maximum likelihood algo-rithm produce clean reconstructed images compared to the conjugate gradient algorithm.
However, all three algorithms experience the so-called superresolution effect in
the presence of noise. A way to prevent suprereolving a blurred image is suggested.

Item Type: Thesis - PhD
Authors/Creators:Law, BNF
Copyright Holders: The Author
Copyright Information:

Copyright 1996 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

Additional Information:

Examines ways to compensate for the effects of atmospheric turbulence on the images obtained from a ground-based telescope, to provide a good quality image. Two approaches are proposed, namely the adaptive optics and the post-detection processing approaches. Thesis (Ph.D.)--University of Tasmania, 1997. Includes bibliographical references. Examines ways to compensate for the effects of atmospheric turbulence on the images obtained from a ground-based telescope, to provide a good quality image. Two approaches are proposed, namely the adaptive optics and the post-detection processing approaches

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