The action of an affine fractal transform or (local) Iterated Function System with gray-level Maps (IFSM) on a function f(x) induces a simple mapping on its expansion coefficients, cij, in the Haar wavelet basis. This is the basis of the discrete fractal-wavelet transform, where subtrees of the wavelet coefficient tree are scaled and copied to lower subtrees. Such transforms, which we shall also refer to as IFS on wavelet coefficients (IFSW), were introduced into image processing with other (compactly supported) wavelet basis sets in an attempt to remove the blocking artifacts that plague standard IFS block- encoding algorithms.
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