Conjugate gradient Mojette reconstruction

Myriam Servieres; Jerome Idier; Niccolas Normand; Jean-Pierre Guedon

doi:10.1117/12.593399

29 April 2005 Conjugate gradient Mojette reconstruction

Myriam Servieres, Jerome Idier, Niccolas Normand, Jean-Pierre Guedon

Proceedings Volume 5747, Medical Imaging 2005: Image Processing; (2005) https://doi.org/10.1117/12.593399
Event: Medical Imaging, 2005, San Diego, California, United States

Abstract

Iterative 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.

Citation Download Citation

Myriam Servieres, Jerome Idier, Niccolas Normand, and Jean-Pierre Guedon "Conjugate gradient Mojette reconstruction", Proc. SPIE 5747, Medical Imaging 2005: Image Processing, (29 April 2005); https://doi.org/10.1117/12.593399

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