Approximating Linear Image Operations in the Wavelet Domain

Wavelet based methods get more and more widely used in image processing applications. This increases the need for standard image operations to be performed in the wavelet domain. As the wavelet transform lacks some basic properties such as shift invariance and a convolution theorem similar to the Fourier transform, this turns out to be a non trivial task. This work presents a strategy to implement linear image operations in the wavelet domain. Experimental results are shown for the pixel-wise product, the shift operation and the convolution. Because of good results for the convolution, this operation is optimised for timing performance to show that it is a competitive alternative to the pixel based operation.