Applying rapid numerical approximation of convolutions with filters for image processing purposes

A computer implemented method for applying a numerical approximation of a convolution of image I as represented by hierarchical signals al of level l with filter f, said method including the steps of: generating a forward transformation by applying a convolution between al and kernel h1 for each level of hierarchy l and by down-sampling the result of convolved al and h1; generating a backward transformation by applying, for each level of hierarchy l, a convolution between kernel h2 and an up-sampled forward transformation and combining the result with a convolution of al with kernel g; and combining the forward transformation with the backward transformation, to yield â0 being an approximation of a convolution between a and f, wherein kernels h1, h1, and g are optimized kernels of filter f.