Blind Image Deconvolution Using The Sylvester Matrix

Blind image deconvolution refers to the process of determining both an exact image and the blurring function from its inexact image. This thesis presents a solution of the blind image deconvolution problem us- ing polynomial computations. The proposed solution does not require prior knowledge of the blurring function or noise level. Blind image deconvolution is needed in many applications, such as astronomy, re- mote sensing and medical X-ray, where noise is present in the exact image and blurring function. It is shown that the Sylvester resultant matrix enables the blurring function to be calculated using approx- imate greatest common divisor computations, rather than greatest common divisor computations. A developed method for the com- putation of an approximate greatest common divisor of two inexact univariate polynomials is employed here, to identify arbitrary forms of the blurring function. The deblurred image is then calculated by de- convolving the computed blurring function from the degraded image, using polynomial division. Moreover, high performance computing is considered to speed up the calculation performed in the spatial do- main. The effectiveness of the proposed solution is demonstrated by experimental results for the deblurred image and the blurring func- tion, and the results are compared with the state-of-the-art image deblurring algorithm.