À trous wavelet transform and coefficients whitening. Two top rows: chained convolutions c_s(k) of the input image c₀(k) with à trous kernels dilated by a factor of two at each step. The left half of each panel corresponds to regular convolutions; the right half to bilateral filtering. Two middle rows: corresponding wavelet coefficients w_s + 1(k)=c_s(k)−c_s + 1(k), that is the difference between successive convolutions or bilateral filterings. The last coefficient is the result of the last convolution or bilateral filtering. The original image (c₀(k), left) is the sum of all coefficients. The bilateral transform preserves the edges in the coarse images (top rows). Two bottom rows: whitened coefficients, i.e., normalized to the local power. The filtered image (left) is the sum of all whitened coefficients. For visualization purposes, the convolutions and the coefficients are displayed using two different color scales.