Jian Lu, Lin Huang, Xiaoxia Liu, Ning Xie, Qingtang Jiang, Yuru Zou
{"title":"通过基于补丁的张量对数 Schatten-p 最小化实现三维泊松图像去模糊","authors":"Jian Lu, Lin Huang, Xiaoxia Liu, Ning Xie, Qingtang Jiang, Yuru Zou","doi":"10.1088/1361-6420/ad40c9","DOIUrl":null,"url":null,"abstract":"\n In medical and biological image processing, multi-dimensional images are often corrupted by blur and Poisson noise. In this paper, we first propose a new tensor logarithmic Schatten-$p$ (t-log-$S_p$) low-rank measure and a tensor iteratively reweighted Schatten-$p$ minimization (t-IRSpM) algorithm for minimizing such measure. Furthermore, we adopt this low-rank measure to regularize the non-local tensors formed by similar 3D image patches and develop a patch-based non-local low-rank model. The data fidelity term of the model characterizes the Poisson noise distribution and blur operator. The optimization model is further solved by an alternating minimization technique combined with variable splitting. Experimental results tested on 3D fluorescence microscope images show that the proposed patch-based tensor logarithmic Schatten-$p$ minimization (TLSpM) method outperforms state-of-the-art methods in terms of image evaluation metrics and visual quality.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization\",\"authors\":\"Jian Lu, Lin Huang, Xiaoxia Liu, Ning Xie, Qingtang Jiang, Yuru Zou\",\"doi\":\"10.1088/1361-6420/ad40c9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n In medical and biological image processing, multi-dimensional images are often corrupted by blur and Poisson noise. In this paper, we first propose a new tensor logarithmic Schatten-$p$ (t-log-$S_p$) low-rank measure and a tensor iteratively reweighted Schatten-$p$ minimization (t-IRSpM) algorithm for minimizing such measure. Furthermore, we adopt this low-rank measure to regularize the non-local tensors formed by similar 3D image patches and develop a patch-based non-local low-rank model. The data fidelity term of the model characterizes the Poisson noise distribution and blur operator. The optimization model is further solved by an alternating minimization technique combined with variable splitting. Experimental results tested on 3D fluorescence microscope images show that the proposed patch-based tensor logarithmic Schatten-$p$ minimization (TLSpM) method outperforms state-of-the-art methods in terms of image evaluation metrics and visual quality.\",\"PeriodicalId\":50275,\"journal\":{\"name\":\"Inverse Problems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Inverse Problems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6420/ad40c9\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6420/ad40c9","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization
In medical and biological image processing, multi-dimensional images are often corrupted by blur and Poisson noise. In this paper, we first propose a new tensor logarithmic Schatten-$p$ (t-log-$S_p$) low-rank measure and a tensor iteratively reweighted Schatten-$p$ minimization (t-IRSpM) algorithm for minimizing such measure. Furthermore, we adopt this low-rank measure to regularize the non-local tensors formed by similar 3D image patches and develop a patch-based non-local low-rank model. The data fidelity term of the model characterizes the Poisson noise distribution and blur operator. The optimization model is further solved by an alternating minimization technique combined with variable splitting. Experimental results tested on 3D fluorescence microscope images show that the proposed patch-based tensor logarithmic Schatten-$p$ minimization (TLSpM) method outperforms state-of-the-art methods in terms of image evaluation metrics and visual quality.
期刊介绍:
An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution.
As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others.
The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.