Restoration of atmospheric turbulence degraded video using kurtosis minimization and motion compensation

It has been long recognized that atmospheric turbulence degrades the quality of images and video sequences. Stationary objects being observed through the atmosphere can appear blurred and waver spatially as if they are in motion. This phenomenon is well recognized, especially in astronomy. The degradation arises from the complicated, random fluctuations in the refractive index of the air, caused by fluctuations in temperature. In this thesis, the fundamental theory of turbulence such as the Kolmogorov law is reviewed. It is also shown that the point spread function (PSF) of the turbulence can be derived from the physics equations that describe atmospheric turbulence.; Atmospheric turbulence degradation is usually modeled as a linear convolution. The turbulence is dynamic and random in nature. The blurring parameter of the PSF of the turbulence is dependent on altitude, temperature, the rate of energy per mass dissipated by viscous friction, the sheer rate of the wind, and so on. Information about those turbulence conditions is often not available. Thus, the exact PSF of the turbulence blur is generally unknown in practice. Consequentially, blind image deconvolution technique is used in such a context. Blind image deconvolution is well known to be an ill-posed problem. Certain assumptions about the image and/or the blur must be made in order to find a solution. It has been observed that the kurtosis of the blurred (smoothed) image is often higher than an unblurred version. This observation is studied and justified using a frequency domain analysis where kurtosis is first represented and then interpreted. An image can be decomposed into a low frequency component and a high frequency component. It is found that the kurtosis of an image is dominated by the interaction of the low frequency and high frequency components. Blurring alters the interaction and tends to increase the kurtosis. In addition to the theoretical analysis, experiments are conducted to verify that the smoothed image has higher kurtosis. This important observation forms the basis for the new blind deconvolution method. Kurtosis can be viewed as a metric to measure the quality of the resorted image without having the original image. In simulations, when an original image is available, one can use peak signal-to-noise ratio (PSNR), to determine the restored image that has the highest PSNR (PSNR maximization) to estimate the blurring parameter. Kurtosis minimization based blur identification works as following: given the functional form of the blur and an estimate of the parameter space, the parameter is searched by minimizing the kurtosis of the restored image. The restored image that has minimal kurtosis is used as the final estimate of the true image and the corresponding parameter is the identified blurring parameter. In many simulations, kurtosis minimization gives the same result as PSNR maximization. Kurtosis minimization is a generally applicable blur identification method. It has been tested on a variety of blurs including Gaussian blur, linear motion blur, out-of-focus blur, averaging blur and atmospheric turbulence blurs. In many experiments on standard test images, kurtosis minimization is able to give perfect estimation at different levels of noise. Moreover, it is compared with generalized cross validation (GCV) based blur identification on atmospheric turbulence blurs, which is the main application in this thesis work.; Besides blurring, turbulence also introduces geometric distortion in the video since the turbulence is time-varying. (Abstract shortened by UMI.)...