1. A computer implemented method to generate a filtered image, the method comprising: receiving image I as represented by input pixels a l where l denotes a level in a hieracarchy; generating with a processor, a forward transformation by applying a convolution between the input pixels a l and kernel h 1 for each level of hierarchy l and by down-sampling the result of convolved a l and h 1 , generating a backward transformation by applying, for each level of hierarchy l, a convolution between kernel h 2 and an up-sampled forward transformation and combining the result with a convolution of a l with kernel g; generating the filtered image by combining the forward transformation with the backward transformation, to yield approximate convolution pixels â 0 ,wherein the approximate convolution pixels â 0 are an approximation of a convolution between a 1 and a filter f, wherein kernels h 1 , h 2 , and g are optimized kernels of the filter f, and wherein generating the filtered image has a lower computational cost compared to generating the filtered image using an unapproximated convolution; and displaying the filtered image.