{"id":{"repo_id":"duquesne","oai_identifier":"oai:dsc.duq.edu:etd-2161"},"canonical_url":"https://search.dev.ndltd.org/etd/duquesne/oai:dsc.duq.edu:etd-2161","repository":{"repo_id":"duquesne","name":"Duquesne","base_url":"https://dsc.duq.edu/do/oai/"},"display":{"title":"Sparse and Redundant Image Representations Using Adaptive Dictionaries in Digital Image Denoising","abstract":"Digital image denoising is a widely know problem in image processing. In this work, we focus on removing additive white Gaussian noise from a given image. We use a denoising method that was extended from the Sparseland model. This method builds sparse image patch representations using redundant dictionaries and has been shown to denoise images fairly well. We look to improve this method by adapting the dictionaries to more accurately represent specific image features. The image features were chosen to be the details, textures, and smooth regions of the image. Two different dictionaries were tested, the Discrete Cosine Transform and a learned dictionary based off of the noisy image patches. The dictionary's patch size was also varied to find the optimal patch size for denoising each image feature. Numerical and visual comparisons show the promise of this method improvement.","abstract_html":"Digital image denoising is a widely know problem in image processing. In this work, we focus on removing additive white Gaussian noise from a given image. We use a denoising method that was extended from the Sparseland model. This method builds sparse image patch representations using redundant dictionaries and has been shown to denoise images fairly well. We look to improve this method by adapting the dictionaries to more accurately represent specific image features. The image features were chosen to be the details, textures, and smooth regions of the image. Two different dictionaries were tested, the Discrete Cosine Transform and a learned dictionary based off of the noisy image patches. The dictionary's patch size was also varied to find the optimal patch size for denoising each image feature. Numerical and visual comparisons show the promise of this method improvement.","abstract_has_math":false,"creators":["Sano, Teresa"],"institution":null,"degree_name":"MS","degree_level":"Immediate Access","degree_discipline":"Computational Mathematics","degree_department":null,"school":null,"contributors":["Stacey Levine","Carl Toews","Mark Mazur"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-01-01T08:00:00Z","date_published":"2009-01-01T08:00:00Z","updated_at":"2026-07-24T02:10:29Z","subjects":["image processing","denoising","sparsity","geometric features"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dsc.duq.edu/etd/1145","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stacey Levine","Carl Toews","Mark Mazur"]},{"key":"dc:creator","label":"Author","values":["Sano, Teresa"]}]},{"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":["image processing","denoising","sparsity","geometric features"]}]},{"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/1145"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Digital image denoising is a widely know problem in image processing. In this work, we focus on removing additive white Gaussian noise from a given image. We use a denoising method that was extended from the Sparseland model. This method builds sparse image patch representations using redundant dictionaries and has been shown to denoise images fairly well. We look to improve this method by adapting the dictionaries to more accurately represent specific image features. The image features were chosen to be the details, textures, and smooth regions of the image. Two different dictionaries were tested, the Discrete Cosine Transform and a learned dictionary based off of the noisy image patches. The dictionary's patch size was also varied to find the optimal patch size for denoising each image feature. Numerical and visual comparisons show the promise of this method improvement."]},{"key":"dc:title","label":"Title","values":["Sparse and Redundant Image Representations Using Adaptive Dictionaries in Digital Image Denoising"]}]}],"canonical_facts":{"dc:contributor":["Stacey Levine","Carl Toews","Mark Mazur"],"dc:creator":["Sano, Teresa"],"dc:date.available":["2018-08-03T07:00:00Z"],"dc:description.abstract":["Digital image denoising is a widely know problem in image processing. In this work, we focus on removing additive white Gaussian noise from a given image. We use a denoising method that was extended from the Sparseland model. This method builds sparse image patch representations using redundant dictionaries and has been shown to denoise images fairly well. We look to improve this method by adapting the dictionaries to more accurately represent specific image features. The image features were chosen to be the details, textures, and smooth regions of the image. Two different dictionaries were tested, the Discrete Cosine Transform and a learned dictionary based off of the noisy image patches. The dictionary's patch size was also varied to find the optimal patch size for denoising each image feature. Numerical and visual comparisons show the promise of this method improvement."],"dc:identifier":["https://dsc.duq.edu/etd/1145"],"dc:language":["English"],"dc:subject":["image processing","denoising","sparsity","geometric features"],"dc:title":["Sparse and Redundant Image Representations Using Adaptive Dictionaries in Digital Image Denoising"],"thesis:degree_discipline":["Computational Mathematics"],"thesis:degree_level":["Immediate Access"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T02:10:29Z"}