Open AccessConjugate gradient Mojette reconstruction
Author(s) -
Myriam Servières,
Jérôme Idier,
Nicolas Normand,
Jeanpierre Guédon
Publication year - 2005
Publication title -
proceedings of spie, the international society for optical engineering/proceedings of spie
Language(s) - English
Resource type - Conference proceedings
SCImago Journal Rank - 0.192
H-Index - 176
eISSN - 1996-756X
pISSN - 0277-786X
DOI - 10.1117/12.593399
Subject(s) - conjugate gradient method , computer science , toeplitz matrix , iterative reconstruction , algorithm , iterative method , context (archaeology) , tomographic reconstruction , projection (relational algebra) , geometry , mathematics , computer vision , paleontology , pure mathematics , biology
International audienceIterative methods are now recognized as powerful tools to solve inverse problems such as tomographic reconstruction. In this paper, the main goal is to present a new reconstruction algorithm made from two components. An iterative algorithm, namely the Conjugate Gradient (CG) method, is used to solve the tomographic problem in the least square (LS) sense for our specific discrete Mojette geometry. The results are compared (with the same geometry) to the corresponding Mojette Filtered Back Projection (FBP) method. In the fist part of the paper, we recall the discrete geometry used to define the projection M and backprojection M* operators. In the second part, the CG algorithm is presented within the context of the Mojette geometry. Noise is then added onto these Mojette projections with respect to the sampling and reconstructions are performed. Finally the Toeplitz block Toeplitz (TBT) character of M*M is demonstrated
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