{"title":"有限投影CT图像重构的1- 1范数和1- 0范数正则化算法。","authors":"Xiezhang Li, Guocan Feng, Jiehua Zhu","doi":"10.1155/2020/8873865","DOIUrl":null,"url":null,"abstract":"<p><p>The <i>l</i> <sub>1</sub>-norm regularization has attracted attention for image reconstruction in computed tomography. The <i>l</i> <sub>0</sub>-norm of the gradients of an image provides a measure of the sparsity of gradients of the image. In this paper, we present a new combined <i>l</i> <sub>1</sub>-norm and <i>l</i> <sub>0</sub>-norm regularization model for image reconstruction from limited projection data in computed tomography. We also propose an algorithm in the algebraic framework to solve the optimization effectively using the nonmonotone alternating direction algorithm with hard thresholding method. Numerical experiments indicate that this new algorithm makes much improvement by involving <i>l</i> <sub>0</sub>-norm regularization.</p>","PeriodicalId":47063,"journal":{"name":"International Journal of Biomedical Imaging","volume":"2020 ","pages":"8873865"},"PeriodicalIF":3.3000,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/8873865","citationCount":"2","resultStr":"{\"title\":\"An Algorithm of <i>l</i> <sub>1</sub>-Norm and <i>l</i> <sub>0</sub>-Norm Regularization Algorithm for CT Image Reconstruction from Limited Projection.\",\"authors\":\"Xiezhang Li, Guocan Feng, Jiehua Zhu\",\"doi\":\"10.1155/2020/8873865\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The <i>l</i> <sub>1</sub>-norm regularization has attracted attention for image reconstruction in computed tomography. The <i>l</i> <sub>0</sub>-norm of the gradients of an image provides a measure of the sparsity of gradients of the image. In this paper, we present a new combined <i>l</i> <sub>1</sub>-norm and <i>l</i> <sub>0</sub>-norm regularization model for image reconstruction from limited projection data in computed tomography. We also propose an algorithm in the algebraic framework to solve the optimization effectively using the nonmonotone alternating direction algorithm with hard thresholding method. Numerical experiments indicate that this new algorithm makes much improvement by involving <i>l</i> <sub>0</sub>-norm regularization.</p>\",\"PeriodicalId\":47063,\"journal\":{\"name\":\"International Journal of Biomedical Imaging\",\"volume\":\"2020 \",\"pages\":\"8873865\"},\"PeriodicalIF\":3.3000,\"publicationDate\":\"2020-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/2020/8873865\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Biomedical Imaging\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2020/8873865\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2020/1/1 0:00:00\",\"PubModel\":\"eCollection\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, BIOMEDICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Biomedical Imaging","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2020/8873865","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/1/1 0:00:00","PubModel":"eCollection","JCR":"Q2","JCRName":"ENGINEERING, BIOMEDICAL","Score":null,"Total":0}
An Algorithm of l1-Norm and l0-Norm Regularization Algorithm for CT Image Reconstruction from Limited Projection.
The l1-norm regularization has attracted attention for image reconstruction in computed tomography. The l0-norm of the gradients of an image provides a measure of the sparsity of gradients of the image. In this paper, we present a new combined l1-norm and l0-norm regularization model for image reconstruction from limited projection data in computed tomography. We also propose an algorithm in the algebraic framework to solve the optimization effectively using the nonmonotone alternating direction algorithm with hard thresholding method. Numerical experiments indicate that this new algorithm makes much improvement by involving l0-norm regularization.
期刊介绍：
The International Journal of Biomedical Imaging is managed by a board of editors comprising internationally renowned active researchers. The journal is freely accessible online and also offered for purchase in print format. It employs a web-based review system to ensure swift turnaround times while maintaining high standards. In addition to regular issues, special issues are organized by guest editors. The subject areas covered include (but are not limited to):
Digital radiography and tomosynthesis
X-ray computed tomography (CT)
Magnetic resonance imaging (MRI)
Single photon emission computed tomography (SPECT)
Positron emission tomography (PET)
Ultrasound imaging
Diffuse optical tomography, coherence, fluorescence, bioluminescence tomography, impedance tomography
Neutron imaging for biomedical applications
Magnetic and optical spectroscopy, and optical biopsy
Optical, electron, scanning tunneling/atomic force microscopy
Small animal imaging
Functional, cellular, and molecular imaging
Imaging assays for screening and molecular analysis
Microarray image analysis and bioinformatics
Emerging biomedical imaging techniques
Imaging modality fusion
Biomedical imaging instrumentation
Biomedical image processing, pattern recognition, and analysis
Biomedical image visualization, compression, transmission, and storage
Imaging and modeling related to systems biology and systems biomedicine
Applied mathematics, applied physics, and chemistry related to biomedical imaging
Grid-enabling technology for biomedical imaging and informatics
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