ساخت تصویر و مکانیزم (سازکار) توموگرافی دانش محور

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی کاربردی، دانشکده ریاضی، دانشگاه علم و صنعت ایران، تهران، ایران

چکیده

در این مطالعه مسأله ساخت تصویر (مسأله وارون) و ارتباط معنایی آن با رده بزرگی از مسائل کاربردی و مهندسی تبیین می‌شود. سازوکار توموگرافی که نمونه‌ای از مسأله ساخت تصویر است، تشریح می‌گردد. پیرامون وجود جواب و یکتایی آن و همچنین تکنیک‌های منظم‌سازی بحث می‌شود. به منظور مصورسازی مفاهیم انتزاعی، فرآیند دیجیتالی تصویر برداری اشعه ایکس با نرم‌افزار ‎MATLAB‎ ارائه می‌شود. تکنیک‌های بازسازی تصویر، براساس تبدیلات معکوس رادون و فوریه و همچنین روش‌های جبری تشریح می‌گردند. اثر انتخاب تعداد جهت‌ها در توموگرافی و نویز تجمعی در داده‌ها بر کیفیت تصویر بازسازی شده بررسی می‌گردد. نتایج عددی و مقایسه تصویرهای بازسازی شده توسط روش‌های مختلف، بر توانمندی ویژه تکنیک‌های جبری در بازسازی تصویر صحه می‌گذارند. علاوه بر این نشان داده می‌شود که در روش‌های جبری می‌توان ویژگی‌های مطلوبی همچون مثبت بودن و همواری را برای تصویر بازسازی شده لحاظ کرد که ثاثیر بسزایی در کاهش خطای تقریب دارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Image Reconstruction and Knowledgebase Tomography Mechanism

نویسندگان [English]

  • Laya Afzalipour
  • Touraj Nikazad
Department of Applied Mathematics, Faculty of Mathematics, Iran University of Science & Technology, Tehtan, Iran
چکیده [English]

In this study, the problem of image reconstruction (Inverse Problem) and its semantic relationship

with a large range of applied and engineering problems are explained. The mechanism of tomographic

which is an example of the image reconstruction problem is described. The existence and uniqueness of

solutions and also regularization techniques are discussed. In order to better imagine abstract concepts, the process of digital X-ray imaging is presented using MATLAB. Image reconstruction techniques

are described by Radon and Fourier transforms and algebraic methods. The effects of selecting the number of angles in tomography and additive noise in the data, on the quality of the reconstructed image are investigated. The numerical results and the comparison of images reconstructed by different methods confirm the special ability of algebraic techniques in image reconstruction. In addition, it is shown that in algebraic methods, desirable features such as positivity and smoothness can be considered for the reconstructed image, which has a significant effect on reducing the approximation error.

کلیدواژه‌ها [English]

  • Image Reconstruction
  • Regularization
  • Algebraic Image Reconstruction Technique
  • Radon Inverse transform
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