Graduate Thesis Or Dissertation
 

Overcoming the singularity problem in digital image restoration

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  • A recorded image is a degraded version of an original image. The process of removing the degradations is called restoration. Two types of degradations are considered in this thesis: namely, linear motion and defocused lens blurrings. Using the direct deconvolution technique to restore blurred images is impossible if the blurring matrix does not have an inverse. Such matrix is called a singular matrix. Facing this problem, researchers dropped the deconvolution approach and resorted to other algorithms such as the pseudoinverse, a neural network, and a regularized iterative approaches. It is the aim of this work to propose a new heuristic algorithm that overcomes the singularity problem using direct deconvolution and an iterative scheme. To test my algorithm against the other three algorithms computer simulations were performed, on blurred images, in a noise-free and noisy environments. It was found that in a noise-free environment my algorithm is superior to the other algorithms in terms of error and time consumption. In a noisy environment, my algorithm fails to restore comprehensible images.
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