Restoration of Images Taken Through a Turbulent Medium

This thesis investigates the problem of how information contained in multiple, short exposure images of the same scene taken through (and distorted by) a turbulent medium (turbulent atmosphere or moving water surface) may be extracted and combined to produce a single image with superior quality and higher resolution. This problem is generally termed image restoration. It has many applications in fields as diverse as remote sensing, military intelligence, surveillance and recognition at a long distance, and other imaging problems which suffer from turbulent media, including e.g. the atmosphere and moving water surface. Wide-area/near-to-ground imaging (through atmosphere) and water imaging are the two main focuses of this thesis. The central technique used to solve these problems is speckle imaging, which is used to process a large number of images of the object with short exposure times such that the turbulent effect is frozen in each frame. A robust and efficient method using the bispectrum is developed to recover an almost diffraction-limited sharp image using the information contained in the captured short exposure images. Both the accuracy and the potential of these new algorithms have been investigated. Motivated by the lucky imaging technique which was used to select superior frames for astronomical imaging application, a new and more efficient technique is proposed. This technique is called lucky region, and it is aimed at selecting image regions with high quality as opposed to selecting a whole image as a lucky image. A new algorithm using bicoherence is proposed for lucky region selection. Its performance, as well as practical factors that may affect the performance, are investigated both theoretically and empirically. To further improve the quality of the recovered clean image after the speckle bispectrum processing, we also investigate blind deconvolution. One of the original contributions is to use natural image sparsity as a prior knowledge for the turbulence image restoration problem. A new algorithm is proposed and its performance is validated experimentally. The new methods are extended to the case of water imaging: restoration of images distorted by moving water waves. It is shown that this problem can be effectively solved by techniques developed in this thesis. Possible practical applications include various forms of ocean observation