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1 Journal of Medical Informatics & Technologies

1 2007

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Hurwitz-Radon operator in monochromatic medical image reconstruction

Jakóbczak D., Kosiński W.

Journal of Medical Informatics & Technologies

2007

Vol. 11

69--78

In this paper the method, dedicated for medical images reconstruction, will be presented. One of them called the method of the Hurwitz-monochromatic (e.g. black and white) images. The method is based on a family of Hurwitz-Radon matrices. The matrices possess columns composed of orthonormal vectors. The operator of Hurwitz-Radon (OHR), built from that matrices, is described. It is shown how to create the orthogonal and discrete OHR and how to use it in a process of curve interpolation. The method needs suitable choice of nodes, i.e. points of the curve to be compressed: they should be equidistance in one of coordinates. Application of MHR gives a high level of compression (up to 99 %) and a very good interpolation accuracy in the process of reconstruction of contours. Its use in the computer tomography is also effective. Orthogonal OHR can be regarded as a linear and discrete model in the supervised (machine) learning [5]. It is shown how to use it in approximation of data. Created from the family of N-1 HR matrices and completed with the identical matrix, system of matrices is orthogonal only for vector spaces of dimensions N=2,4,8. Orthogonality of columns and rows is very important and significant for stability and high precision of calculations.