NEWS & EVENTS
Neuroscience Modules
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    Neuroscience Modules

    Image Reconstruction in Emission Tomography I: Non-iterative Methods
    Image Reconstruction in Emission Tomography I: Supporting Documents 


    Module Author: Edward J. Soares
    Author Contact: esoares@holycross.edu
    Funded By: W.M. Keck Foundation

     

    The overall goal of this module is to show students the connection between physical problems in medical imaging and theoretical problems in mathematics. In particular, students will learn how such a physical problem can be translated into the language of mathematics, how one then uses standard mathematical techniques to solve the problem, and finally how the mathematical solution is re-translated back into a physical interpretation. As with all problems involving mathematical modelling of physical phenomena, it is important to evaluate the methods used and results obtained, and so students will also try to assess the work they have conducted.

    This module is intended for a general audience with a background in singleand multi-variable calculus, and linear algebra. Although no computer formal programming skills are required, students should be comfortable using MAPLE and MATLAB, as these programs are used in the latter sections. The only mathematical concept that students might not have been exposed to would be Singular Value Decomposition (SVD) [5, 6]. This topic will be extensively reviewed within the module, however students should have taken a course in Numerical Methods or Numerical Linear Algebra in order to better learn this important concept. Also, after having completed this module, students will be able to extend and apply the concepts and skills learned to the Image Reconstruction in Emission Tomography II. Iterative Methods module. In that module, students will study iterative method for solving linear systems and how they can be applied to the same image reconstruction problem. The flexibility of this module lies in the fact that it is essentially self-contained, except for the required mathematical knowledge. Ideally, it will be used as an integrated component in a section of a course that focuses on the modelling physical phenomena using linear systems of equations. Also, it would be best used by incorporating both classroom lectures, group work and computer lab sessions into the presentation of the material.

    Image Reconstruction in Emission Tomography II: Iterative Methods
    Image Reconstruction in Emission Tomography II: Supporting Documents 


    Module Author: Edward J. Soares
    Author Contact: esoares@holycross.edu
    Funded By: W.M. Keck Foundation

     

    The overall goal of this module is to show students the connection between physical problems in medical imaging and theoretical problems in mathematics. In particular, students will learn how such a physical problem can be translated into the language of mathematics, how one then uses standard mathematical techniques to solve the problem, and finally how the mathematical solution is re-translated back into a physical interpretation. As with all problems involving mathematical modelling of physical phenomena, it is important to evaluate the methods used and results obtained, and so students will also try to assess the work they have conducted.

    This module is intended for a general audience with a background in singleand multi-variable calculus, and linear algebra. Although no computer formal programming skills are required, students should be comfortable using MAPLE and MATLAB, as these programs are used in the latter sections. The only mathematical concepts that students might not have been exposed to would be the iterative solution methodologies themselves [5, 6]. These topics will be extensively reviewed within the module, however students should have taken a course in Numerical Methods or Numerical Linear Algebra in order to better learn these important concepts. Also, after having completed this module, students will be able to extend and apply the concepts and skills learned to the Image Reconstruction in Emission Tomography I. Non-iterative Methods module. In that module, students will study non-iterative methods for solving linear systems and how they can be applied to the same image reconstruction problem. The flexibility of this module lies in the fact that it is essentially self-contained, except for the required mathematical knowledge. Ideally, it will be used as an integrated component in a section of a course that focuses on the modelling physical phenomena using linear systems of equations. Also, it would be best used by incorporating both classroom lectures, group work and computer lab sessions into the presentation of the material.