Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Silvio Melo: A Rational B-splines Tomographic Reconstruction of the Catalyst Density Distribution Function

Mon, 20 July, 2009, 17:15-18:15, Foyer

A novel method of tomographic reconstruction is presented. Based on the Algebraic Reconstruction Technique (ART), our method represents the density distribution function of the object being reconstructed as a rational B-splines surface. The application focused in this work is the reconstruction of the catalyst density distribution in an FCC cracking unit, called riser, present in any oil refinery. A traditional ART method takes as unknowns the intensity of all the atomic cells (pixels) in the grid where the reconstructed model is supposed to be represented. With the use of weighted control points, and assuming that the density distribution function is smooth, it is possible to reduce the size of the resulting linear system up to 50%, depending on the losses we can tolerate. Since we are using degree-three-rational-functions, the B-splines surface is a C2 type. The control points values are found through a Least Squares method, which subjects the resulting surface in a way that different cross sections density values are summed up as close as possible to the experimental readings (from the gamma-ray tomographer). The family of parallel cross sections is associated with the family of gamma-ray trajectories through the riser, each family forming a different angle with the horizontal line. The adjustment of the weights associated to each control point allows a much better local definition than, say, regular B-splines. That can be done as a second pass. Using phantoms such as the Shepp-Logan we show that the proposed method is very competitive, in some cases even outperforming the traditional one in quality, not only in speed.

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