{"id":{"repo_id":"houston","oai_identifier":"oai:uh-ir.tdl.org:10657/17751"},"canonical_url":"https://search.dev.ndltd.org/etd/houston/oai:uh-ir.tdl.org:10657/17751","repository":{"repo_id":"houston","name":"University of Houston","base_url":"https://uh-ir.tdl.org/server/oai/request"},"display":{"title":"Integration of Model- and Learning-based Methods in Image Restoration","abstract":"Following the spectacular success of deep learning algorithms in image restoration tasks, there is growing interest in exploring how to combine the practical advantages of learning-based methods with the theoretical understanding that comes from model-based approaches. In fact, while deep learning methods often provide state-of-the-art performance, they usually have no performance guarantees and one cannot predict how well they would perform on new data. It is generally expected that the integration of such methods with ideas from model-based strategies could lead to a new generation of more powerful algorithms. Here we focus especially on problems motivated by image restoration tasks that include image inpainting, denoising and deblurring. After reviewing the most prominent strategies proposed in the literature to combine model- and learning-driven methods for problems in image restoration, we introduce two new algorithms designed to combine the interpretability of model-driven methods and the efficiency of learning-driven methods. Our first approach proposes a novel training strategy for deep convolutional neural networks (CNNs) that leverages theoretically concepts from transform domain and sparse representations. Its main idea consists of representing the convolutional kernels as linear combinations of predefined filter dictionaries where the coefficients of the linear combination are the only learnable parameters. We show that, by choosing the dictionaries carefully and imposing sparsity-based constraints motivated by the theory of sparse multiscale representations, this approach offers several potential advantages with respect to conventional CNNs, especially in the situation of small sample size. Our second approach exploits the recently introduced framework of the Implicit Neural Representation (INR), a coordinate-based neural network for imaging problems, which parametrizes images or shapes using a Multi Layer Perception (MLP). We propose a novel INR with a prolate spheroidal wave function (PSWF) as an activation function, taking advantage of ideas from the theory of band-limit function to derive an improved and highly competitive method for image representation and restoration.","abstract_html":"Following the spectacular success of deep learning algorithms in image restoration tasks, there is growing interest in exploring how to combine the practical advantages of learning-based methods with the theoretical understanding that comes from model-based approaches. In fact, while deep learning methods often provide state-of-the-art performance, they usually have no performance guarantees and one cannot predict how well they would perform on new data. It is generally expected that the integration of such methods with ideas from model-based strategies could lead to a new generation of more powerful algorithms. Here we focus especially on problems motivated by image restoration tasks that include image inpainting, denoising and deblurring. After reviewing the most prominent strategies proposed in the literature to combine model- and learning-driven methods for problems in image restoration, we introduce two new algorithms designed to combine the interpretability of model-driven methods and the efficiency of learning-driven methods. Our first approach proposes a novel training strategy for deep convolutional neural networks (CNNs) that leverages theoretically concepts from transform domain and sparse representations. Its main idea consists of representing the convolutional kernels as linear combinations of predefined filter dictionaries where the coefficients of the linear combination are the only learnable parameters. We show that, by choosing the dictionaries carefully and imposing sparsity-based constraints motivated by the theory of sparse multiscale representations, this approach offers several potential advantages with respect to conventional CNNs, especially in the situation of small sample size. Our second approach exploits the recently introduced framework of the Implicit Neural Representation (INR), a coordinate-based neural network for imaging problems, which parametrizes images or shapes using a Multi Layer Perception (MLP). We propose a novel INR with a prolate spheroidal wave function (PSWF) as an activation function, taking advantage of ideas from the theory of band-limit function to derive an improved and highly competitive method for image representation and restoration.","abstract_has_math":false,"creators":["Zhao, Heng"],"institution":"University of Houston","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Labate, Demetrio"],"committee_chairs":[],"committee_members":["Papadakis, Emanuel","Mang, Andreas","Zhang, Ruda"],"year":2024,"date_issued":"2024-05-02","date_published":"2024-05-02","updated_at":"2026-07-24T02:32:12Z","subjects":["neural networks","image restoration","image inpainting","image denoising","implicit neural representation"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10657/17751","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Labate, Demetrio"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Papadakis, Emanuel","Mang, Andreas","Zhang, Ruda"]},{"key":"dc:creator","label":"Author","values":["Zhao, Heng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-07-26T23:33:42Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-05-02"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Houston"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["neural networks","image restoration","image inpainting","image denoising","implicit neural representation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10657/17751"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Following the spectacular success of deep learning algorithms in image restoration tasks, there is growing interest in exploring how to combine the practical advantages of learning-based methods with the theoretical understanding that comes from model-based approaches. In fact, while deep learning methods often provide state-of-the-art performance, they usually have no performance guarantees and one cannot predict how well they would perform on new data. It is generally expected that the integration of such methods with ideas from model-based strategies could lead to a new generation of more powerful algorithms. Here we focus especially on problems motivated by image restoration tasks that include image inpainting, denoising and deblurring. After reviewing the most prominent strategies proposed in the literature to combine model- and learning-driven methods for problems in image restoration, we introduce two new algorithms designed to combine the interpretability of model-driven methods and the efficiency of learning-driven methods. Our first approach proposes a novel training strategy for deep convolutional neural networks (CNNs) that leverages theoretically concepts from transform domain and sparse representations. Its main idea consists of representing the convolutional kernels as linear combinations of predefined filter dictionaries where the coefficients of the linear combination are the only learnable parameters. We show that, by choosing the dictionaries carefully and imposing sparsity-based constraints motivated by the theory of sparse multiscale representations, this approach offers several potential advantages with respect to conventional CNNs, especially in the situation of small sample size. Our second approach exploits the recently introduced framework of the Implicit Neural Representation (INR), a coordinate-based neural network for imaging problems, which parametrizes images or shapes using a Multi Layer Perception (MLP). We propose a novel INR with a prolate spheroidal wave function (PSWF) as an activation function, taking advantage of ideas from the theory of band-limit function to derive an improved and highly competitive method for image representation and restoration."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Integration of Model- and Learning-based Methods in Image Restoration"]}]}],"canonical_facts":{"dc:contributor.advisor":["Labate, Demetrio"],"dc:contributor.committeemember":["Papadakis, Emanuel","Mang, Andreas","Zhang, Ruda"],"dc:creator":["Zhao, Heng"],"dc:date.accessioned":["2024-07-26T23:33:42Z"],"dc:date.issued":["2024-05-02"],"dc:description.abstract":["Following the spectacular success of deep learning algorithms in image restoration tasks, there is growing interest in exploring how to combine the practical advantages of learning-based methods with the theoretical understanding that comes from model-based approaches. 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Its main idea consists of representing the convolutional kernels as linear combinations of predefined filter dictionaries where the coefficients of the linear combination are the only learnable parameters. We show that, by choosing the dictionaries carefully and imposing sparsity-based constraints motivated by the theory of sparse multiscale representations, this approach offers several potential advantages with respect to conventional CNNs, especially in the situation of small sample size. Our second approach exploits the recently introduced framework of the Implicit Neural Representation (INR), a coordinate-based neural network for imaging problems, which parametrizes images or shapes using a Multi Layer Perception (MLP). We propose a novel INR with a prolate spheroidal wave function (PSWF) as an activation function, taking advantage of ideas from the theory of band-limit function to derive an improved and highly competitive method for image representation and restoration."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/10657/17751"],"dc:language.iso":["en"],"dc:subject":["neural networks","image restoration","image inpainting","image denoising","implicit neural representation"],"dc:title":["Integration of Model- and Learning-based Methods in Image Restoration"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["University of Houston"]},"updated_at":"2026-07-24T02:32:12Z"}