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Dictionary Learning For Image Reconstruction Via Numerical Non-Convex Optimization Methods, Lewis M. Hicks
Dictionary Learning For Image Reconstruction Via Numerical Non-Convex Optimization Methods, Lewis M. Hicks
University Honors Theses
This thesis explores image dictionary learning via non-convex (difference of convex, DC) programming and its applications to image reconstruction. First, the image reconstruction problem is detailed and solutions are presented. Each such solution requires an image dictionary to be specified directly or to be learned via non-convex programming. The solutions explored are the DCA (DC algorithm) and the boosted DCA. These various forms of dictionary learning are then compared on the basis of both image reconstruction accuracy and number of iterations required to converge.
Curvelets And The Radon Transform, Jill Dickerson
Curvelets And The Radon Transform, Jill Dickerson
Electronic Theses and Dissertations
Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial …
Efficient Cone Beam Reconstruction For The Distorted Circle And Line Trajectory, Souleymane Konate
Efficient Cone Beam Reconstruction For The Distorted Circle And Line Trajectory, Souleymane Konate
Electronic Theses and Dissertations
We propose an exact filtered backprojection algorithm for inversion of the cone beam data in the case when the trajectory is composed of a distorted circle and a line segment. The length of the scan is determined by the region of interest , and it is independent of the size of the object. With few geometric restrictions on the curve, we show that we have an exact reconstruction. Numerical experiments demonstrate good image quality.