A Computationally Efficient Algorithm for Exponential B-Splines Based on Difference/IIR Filter Approach

Takeshi ASAHI  Koichi ICHIGE  Rokuya ISHII  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.6   pp.1265-1273
Publication Date: 2002/06/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Papers Selected from 2001 International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2001))
B-spline,  exponential spline,  decomposition,  reconstruction,  

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This paper proposes a fast method for the calculation of exponential B-splines sampled at regular intervals. This algorithm is based on a combination of FIR and IIR filters which enables a fast decomposition and reconstruction of a signal. When complex values are selected for the parameters of the exponentials, complex trigonometric functions are obtained. Only the real part of these functions are used for the interpolation of real signals, leading less bandlimited signals when they are compared with the polynomial B-spline counterparts. These characteristics were verified with 1-D and 2-D examples. This paper also discusses the effectiveness of exponential B-splines, when they are applied to image processing.