Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.07
{"title":"Adaptively weighted difference model of anisotropic and isotropic total variation for image denoising","authors":"","doi":"10.23952/jnva.7.2023.4.07","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.07","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83103157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.03
{"title":"Weighted-type image segmentation model via coupling heat kernel convolution with high-order total variation","authors":"","doi":"10.23952/jnva.7.2023.4.03","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.03","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82991406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.02
{"title":"Sparse broadband beamformer design via proximal optimization Techniques","authors":"","doi":"10.23952/jnva.7.2023.4.02","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.02","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"428 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75886191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.05
{"title":"Multitemporal image cloud removal using group sparsity and nonconvex low-rank approximation","authors":"","doi":"10.23952/jnva.7.2023.4.05","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.05","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"22 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84492041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.04
Xueding Zhang, Zhemin Li, Hongxia Wang
. Over the past few years, deep learning methods have emerged as powerful image denoising tools. Among them, unsupervised deep learning without external training data is more practical and challenging. Reducing noisy overfitting is challenging due to single-image unsupervised learning is prone to overfitting. In this paper, we propose a method named drop-DIP combing Deep Image Prior (DIP) with drop-out for the first time to solve the above problems. In our method, we construct new network training pairs by performing drop-out training on the Bernoulli sampling of the input and output, and then construct a regularization term by using the corrected bias of the output and the generated prior. Finally, update the parameters through the Alternating Direction Method of Multipliers (ADMM) algorithm. Experiments demonstrate that drop-DIP can alleviate the overfitting difficulty in DIP, facilitate the early stopping of the network, and is applicable to different noise models. Furthermore, our method has good performance on Peak Signal to Noise Ratio (PSNR), Structural Similarity (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) metrics validated by two different datasets.
{"title":"Drop-DIP: A single-image denoising method based on deep image prior","authors":"Xueding Zhang, Zhemin Li, Hongxia Wang","doi":"10.23952/jnva.7.2023.4.04","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.04","url":null,"abstract":". Over the past few years, deep learning methods have emerged as powerful image denoising tools. Among them, unsupervised deep learning without external training data is more practical and challenging. Reducing noisy overfitting is challenging due to single-image unsupervised learning is prone to overfitting. In this paper, we propose a method named drop-DIP combing Deep Image Prior (DIP) with drop-out for the first time to solve the above problems. In our method, we construct new network training pairs by performing drop-out training on the Bernoulli sampling of the input and output, and then construct a regularization term by using the corrected bias of the output and the generated prior. Finally, update the parameters through the Alternating Direction Method of Multipliers (ADMM) algorithm. Experiments demonstrate that drop-DIP can alleviate the overfitting difficulty in DIP, facilitate the early stopping of the network, and is applicable to different noise models. Furthermore, our method has good performance on Peak Signal to Noise Ratio (PSNR), Structural Similarity (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) metrics validated by two different datasets.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"22 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73993323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.01
{"title":"Editorial: Special issue on fast algorithms and theories for applications in signal and image processing","authors":"","doi":"10.23952/jnva.7.2023.4.01","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.01","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"97 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80673693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.08
{"title":"Semi-implicit back propagation","authors":"","doi":"10.23952/jnva.7.2023.4.08","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.08","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"3 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84037292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.23952/jnva.7.2023.4.06
{"title":"Absolute value equations with data uncertainty in the $l_1$ and $l_infty$ norm balls","authors":"","doi":"10.23952/jnva.7.2023.4.06","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.4.06","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"207 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75698150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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