Doctor of Philosophy in Engineering

This thesis considers the problem of restoring an image distorted by a linear spatially invariant point spread function PSF and corrupted by noise A principle aim is to develop techniques that are practical and require a minimum amount of prior knowledge The process of deconvolution is attempted using least squares and maximum likelihood iterative algorithms A survey of the literature introduces the main techniques for deconvo lution when the PSF is known and various approaches for achieving blind deconvolution estimating both the PSF and the underlying object from the blurred observation The two main areas of focus for this thesis are accelerating iterative image restoration algorithms and developing blind deconvolution methods for extended objects The rst main contribution is the development of an acceleration technique to speed the rate of convergence of iterative algorithms that use successive approximation The acceleration uses a vector extrapolation approach which eliminates the need to compute the gradient of an objective function or to perform a line search optimisation The performance is comparable to that of conjugate gradient optimisation and an example maximum entropy restoration reduces the number of iterations from to A simple modi cation to the extrapolation allows the acceleration of the Richardson Lucy RL iteration while implicitly imposing the positivity constraint The second contribution is the development of blind deconvolution algorithms that do not require spatial or spectral constraints to produce a solution and can be used on extended objects The key to achieving this is to recognise that the image and PSF estimates may required di erent amounts of restoration By appropriately weighting the update of the image or PSF estimate a suitable result can be produced Methods for achieving this using both joint and alternating variable optimisation are discussed Issues regarding scaling of the variables are also addressed An iterative blind deconvolution method employing the RL algorithm vector extrapo lation and di erent numbers of image and PSF iterations is used to restore a variety of simulated and real images from terrestrial telescopes the Hubble Space Telescope multiframe speckle imaging D wide eld uorescence and confocal microscopes and scanning electron microscopes Methods for coping with Poisson noise corruption and image boundary artifacts are also discussed