Image Data Compression with Three-directional Splines

In this paper we consider a new method for image data compression. It is based on three-directional spline functions of low degree, viz. Piecewise constant functions, and piecewise cubic C-1-functions. In the first case, a Haar wavelet type decomposition can be derived, and combined with standard thresholding techniques. In the second case, due to the fact that a splice basis is given by convolution products, the wavelet decomposition and thresholding can be computed on one factor of the convolution product only. Performance of the proposed method is discussed in section 3 where the reconstructed pictures are compared with the ones produced by the analogous decomposition methods provided by the MATLAB wavelet toolbox.