An Efficient Algorithm for Decomposition and Reconstruction of Images by Box Splines

Takeshi ASAHI  Koichi ICHIGE  Rokuya ISHII  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.8   pp.1883-1891
Publication Date: 2001/08/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Image/Visual Signal Processing
box spline,  B-spline,  decomposition,  reconstruction,  

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This paper proposes a novel fast algorithm for the decomposition and reconstruction of two-dimensional (2-D) signals by box splines. The authors have already proposed an algorithm to calculate the discrete box splines which enables the fast reconstruction of 2-D signals (images) from box spline coefficients. The problem still remains in the decomposition process to derive the box spline coefficients from an input image. This paper first investigates the decomposition algorithm which consists of the truncated geometric series of the inverse filter and the steepest descent method with momentum (SDM). The reconstruction process is also developed to correspond to the enlargement of images. The proposed algorithm is tested for the expansion of several natural images. As a result, the peak signal-to-noise ratio (PSNR) of the reconstructed images became more than 50 dB, which can be considered as enough high level. Moreover, the property of box splines are discussed in comparison with 2-D (the tensor product of) B-splines.