transmission. In this thesis, diffusion based models were used to solve the image restoration problem as these models can simultaneously remove noise, preserve edges and restore lost information. Specifically, numerical schemes were developed and tested for denoising via nonstandard diffusion that are more computationally efficient than the current method. Furthermore, a new model for digital inpainting is proposed based on the nonstandard diffusion model. Numerical results illustrate the effectiveness of both the denoising and inpainting models in image restoration.","abstract_html":"Many fields of study use images to make discoveries about the past, decisions for the present and predictions for the future. Images often acquire degradations such as a blur due to a patient moving during an x-ray or noise picked up through remote sensing imaging equipment. Images may also lose information through compression or</p><p> transmission. In this thesis, diffusion based models were used to solve the image restoration problem as these models can simultaneously remove noise, preserve edges and restore lost information. Specifically, numerical schemes were developed and tested for denoising via nonstandard diffusion that are more computationally efficient than the current method. Furthermore, a new model for digital inpainting is proposed based on the nonstandard diffusion model. Numerical results illustrate the effectiveness of both the denoising and inpainting models in image restoration.","abstract_has_math":false,"creators":["Pirolli, Melissa"],"institution":null,"degree_name":"MS","degree_level":"Immediate Access","degree_discipline":"Computational Mathematics","degree_department":null,"school":null,"contributors":["Stacey Levine","Constance D. Ramirez","Eric Rawdon","Kathleen Taylor"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-01-01T08:00:00Z","date_published":"2004-01-01T08:00:00Z","updated_at":"2026-07-24T02:10:22Z","subjects":["denoising","image processing","image restoration","inpainting","nonstandard diffusion","optimization"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dsc.duq.edu/etd/1049","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stacey Levine","Constance D. Ramirez","Eric Rawdon","Kathleen Taylor"]},{"key":"dc:creator","label":"Author","values":["Pirolli, Melissa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-08-03T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computational Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Immediate Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["denoising","image processing","image restoration","inpainting","nonstandard diffusion","optimization"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dsc.duq.edu/etd/1049"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Many fields of study use images to make discoveries about the past, decisions for the present and predictions for the future. Images often acquire degradations such as a blur due to a patient moving during an x-ray or noise picked up through remote sensing imaging equipment. Images may also lose information through compression or
transmission. In this thesis, diffusion based models were used to solve the image restoration problem as these models can simultaneously remove noise, preserve edges and restore lost information. Specifically, numerical schemes were developed and tested for denoising via nonstandard diffusion that are more computationally efficient than the current method. Furthermore, a new model for digital inpainting is proposed based on the nonstandard diffusion model. Numerical results illustrate the effectiveness of both the denoising and inpainting models in image restoration."]},{"key":"dc:title","label":"Title","values":["Optimization Techniques for Image Restoration"]}]}],"canonical_facts":{"dc:contributor":["Stacey Levine","Constance D. Ramirez","Eric Rawdon","Kathleen Taylor"],"dc:creator":["Pirolli, Melissa"],"dc:date.available":["2018-08-03T07:00:00Z"],"dc:description.abstract":["Many fields of study use images to make discoveries about the past, decisions for the present and predictions for the future. Images often acquire degradations such as a blur due to a patient moving during an x-ray or noise picked up through remote sensing imaging equipment. Images may also lose information through compression or
transmission. In this thesis, diffusion based models were used to solve the image restoration problem as these models can simultaneously remove noise, preserve edges and restore lost information. Specifically, numerical schemes were developed and tested for denoising via nonstandard diffusion that are more computationally efficient than the current method. Furthermore, a new model for digital inpainting is proposed based on the nonstandard diffusion model. Numerical results illustrate the effectiveness of both the denoising and inpainting models in image restoration."],"dc:identifier":["https://dsc.duq.edu/etd/1049"],"dc:language":["English"],"dc:subject":["denoising","image processing","image restoration","inpainting","nonstandard diffusion","optimization"],"dc:title":["Optimization Techniques for Image Restoration"],"thesis:degree_discipline":["Computational Mathematics"],"thesis:degree_level":["Immediate Access"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T02:10:22Z"}