טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMazor Shai
SubjectImage Reconstruction from Generalized Sampled Radon
Transforms
DepartmentDepartment of Electrical Engineering
Supervisor Professor Emeritus Arie Feuer
Full Thesis textFull thesis text - English Version


Abstract

Computerized Tomography is widely used as a medical imaging method for generat- ing the cross-sectional image of an object. The data is generated by illuminating the object from different directions, the transmitted signals pass through the object and then they are collected by a scanner. The radon transform is used for transforming the projection data collected by the scanner into a 2D or 3D cross-section image of the object. In computerized tomography the illumination process is done using by transmitting x-rays through the scanned objects. Since the x-ray exposure is harmful and dangers to the patient being scanned, the need to improve the reconstruction algorithm and shorten the time of exposure needed to perform a computerized to- mography scan is significant. Using generalized sampling and understanding of the properties of the sampled radon transform and its spectrum characteristics we can implement an effective non-uniform sampling and reconstruction schemes that can produce the same resolution using fewer samples.

In this work we studied and analyzed the two-dimensional sampled radon trans- form and its spectrum characteristics. We used this information to implement an effective sampling and reconstruction schemes for the radon transform. In addition, this work introduces both the design and the implementation of an automatic matlab GUI tool for evaluating the efficiency of Fourier reconstruction of images from their generalized sampled Radon transform, using various sampling methods. The tool offers the user a set of features that assist in a research of the sampled radon transform such as finnding the radon transform and the inverse radon transform of an image, finnding the radon transform 2D frequency response, using a generalized sam-

pling matrix for sampling the radon transform and applying filters on the examined images. The study of scanned images enables the introduction of new, non-uniform, sampling and reconstruction schemes. These require fewer samples in comparison to the standard methods used today and thus enable shorting the x-rays exposure time.