A fast algorithm for orthogonalizing polynomialson an arbitrarily shaped region (1997) [3 citations — 1 self]
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by Dr. Ir. W. Philips, Elektronica En, Informatiesystemen Medisip, Wilfried Philips
IEEE Signal Processing Letters. Submitted
http://www.elis.rug.ac.be/ELISgroups/mbv/philips/reports/Pro9601.ps.gz
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Abstract:
This report presents a faster version of the polynomial recursive orthogonalization (PRO) algorithm, which is used in segmented image coding to generate orthonormal base functions on a non-rectangular discrete image. It shows that up to 25 % of the floating point operations can be eliminated by using previously computed results; also, some orthogonalizations can be avoided altogether, because they are guaranteed to produce zero functions. In practice, the PRO implementation in this report is 20 to 25 % faster than the old algorithm and two to three times faster than Gram-Schmidt orthogonalization. 1
Citations
| 45 | Coding of Arbitrarily Shaped Image Segments Based On a Generalized Orthogonal Transform – Gilge, Engelhardt, et al. - 1989 |
| 40 | Second-generation image-coding techniques – Kunt, Ikonomopoulos, et al. - 1985 |
| 11 | Formal properties of orthogonal polynomials in two variables – Jackson - 1936 |
| 4 | A fast algorithm for the generation of orthogonal base functions on an arbitrarily shaped region – Philips - 1992 |
| 4 | Orthogonal base functions on a discrete twodimensional region – Philips - 1992 |
| 1 | uitgave edition – Golub, Loan - 1991 |
