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A very fast Implementation of 2D Iterative Reconstruction Algorithms
, 1996
"... Introduction In the last 15 years the iterative reconstruction methods have gained much attention in the literature [1]. Several methods have been very prominent, such as EM (Expectation Maximization) [2, 3], ART (Algebraic Reconstruction Technique) [4], and LSCG (Least Squares Conjugate Gradient) ..."
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Introduction In the last 15 years the iterative reconstruction methods have gained much attention in the literature [1]. Several methods have been very prominent, such as EM (Expectation Maximization) [2, 3], ART (Algebraic Reconstruction Technique) [4], and LSCG (Least Squares Conjugate Gradient) [5]. Each of the methods formulates the reconstruction problem as a linear set of equations b = Ax , b i = P J \Gamma1 j=1 a i;j x j , where b is an Idimensional vector containing the known sinogram values wrapped into a vector, and x is a Jdimensional vector containing the unknown image to be reconstructed. The matrix A is the system matrix, which contains the weight factors between each of the image pixels and each of the sinogram values, corresponding to line orientations. One problem i
Brain Mapping by Positron Emission Tomography
, 1996
"... In this paper the basis of PET (Positron Emission Tomography) is reviewed, and it is shown that the measured signals can be modelled as the Radon transform of the desired spatial distribution of, e.g., the brain activity. Next, two of the direct reconstruction methods are presented. Both are derived ..."
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In this paper the basis of PET (Positron Emission Tomography) is reviewed, and it is shown that the measured signals can be modelled as the Radon transform of the desired spatial distribution of, e.g., the brain activity. Next, two of the direct reconstruction methods are presented. Both are derived from inversion of the Radon transform. It is shown that the reconstruction can be based on filtering and integration techniques. Another major class of reconstruction techniques is presented, namely the linear algebra based methods, which often are formed as iterative methods. A very fast way of implementing a set of iterative reconstruction techniques is shown along with a set of examples. 1.1 Introduction to PET The PET scanner is based on radioactive tracers. A small dosage of a fi + emitter, such as O15 or C11, is injected into the patient (or the object to be scanned). The fi + emitter will be distributed in the tissue due to the blood circulation. If for instance the brain is t...