Accelerated iterative blind deconvolution

Abstract

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 deconvolution 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 first 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 optimization. The performance is comparable to that of conjugate gradient optimization, and an example maximum-entropy restoration reduces the number of iterations from 1,000 to 27. A simple modification 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 different 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 extrapolation, and different 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, 3D wide-field fluorescence and confocal microscopes, and scanning electron microscopes. Methods for coping with Poisson noise corruption, and image boundary artifacts are also discussed.