Wavelets generated by using discrete singular convolution kernels

This paper explores the connection between wavelet methods and an efficient computational algorithm-the discrete singular convolution (DSC). Many new DSC kernels are constructed and they are identified as wavelet scaling func tions. Two approaches are proposed to generate wavelets from DSC kernels. T wo well known examples, the Canny filter and the Mexican hat wavelet, are f ound to be special cases of the present DSC kernel-generated wavelets. A fa mily of wavelet generators proposed in this paper are found to form an infi nite-dimensional Lie group which has an invariant subgroup of translation a nd dilation. If DSC kernels form an orthogonal system, they are found to sp an a wavelet subspace in a multiresolution analysis.