Browsing by Subject "Inverse Problems"

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Open Access
Deblurring text images affected by multiple kernels
(2018-06) Dizdarer, Tolga
Image deblurring is one of the widely studied and challenging problems in image recovery. It is an estimation problem dealing with restoration of a linearly transformed image that is additional disturbed with noise. In our research, we propose a new method to solve deblurring problems on text images a ected by multiple kernels. In our approach we focus speci cally on almost binary images that have speci c intensity structures. First, we propose a non-convex non-blind deblurring model and provide an e cient algorithm that can restore a text-like image when the blurring kernel is known. Then we provide our alternate setting, the semi-blind problem, where a kernel is determined as a linear combination of multiple kernels. We propose how one can attack the deblurring problem by using dictionaries that are constructed using any prior information about the kernel. We propose a semi-blind deblurring model that can estimate optimal kernel using the elements of the dictionary. We consider a unique algorithm structure that favors regularizing the iterations through scaled parameter values and argue the advantages of this approach. Lastly, we consider some speci c problems that are commonly used in the literature where one can utilize our alternate problem setting. We argue how one can construct a dictionary that can maximize the utility gained by the prior information regarding the blurring process and present the performance of our model in such cases.
Open Access
Signal and image processing algorithms using interval convex programming and sparsity
(2012) Köse, Kıvanç
In this thesis, signal and image processing algorithms based on sparsity and interval convex programming are developed for inverse problems. Inverse signal processing problems are solved by minimizing the ℓ1 norm or the Total Variation (TV) based cost functions in the literature. A modified entropy functional approximating the absolute value function is defined. This functional is also used to approximate the ℓ1 norm, which is the most widely used cost function in sparse signal processing problems. The modified entropy functional is continuously differentiable, and convex. As a result, it is possible to develop iterative, globally convergent algorithms for compressive sensing, denoising and restoration problems using the modified entropy functional. Iterative interval convex programming algorithms are constructed using Bregman’s D-Projection operator. In sparse signal processing, it is assumed that the signal can be represented using a sparse set of coefficients in some transform domain. Therefore, by minimizing the total variation of the signal, it is expected to realize sparse representations of signals. Another cost function that is introduced for inverse problems is the Filtered Variation (FV) function, which is the generalized version of the Total Variation (VR) function. The TV function uses the differences between the pixels of an image or samples of a signal. This is essentially simple Haar filtering. In FV, high-pass filter outputs are used instead of differences. This leads to flexibility in algorithm design adapting to the local variations of the signal. Extensive simulation studies using the new cost functions are carried out. Better experimental restoration, and reconstructions results are obtained compared to the algorithms in the literature