Haar multiresolution decomposition. Starting at the finest level J (the original data-sphere), the approximation and detail coefficients at level J − 1 are computed. This procedure is repeated to decompose the approximation coefficients at level J − 1 (i.e. the approximation function f_J−1), into approximation and detail coefficients at the coarser level J − 2. Repeating this procedure continually, one recovers the multiresolution representation of f_J in terms of the coarsest level approximation f_J0 and all of the detail coefficients.