Adapted Nonlinear Multiresolution Decomposition with Applications in Progressive Lossless Image Coding

We present an adapted nonlinear multiresolution decomposition (with some derivatives) of still images that permits perfect reconstruction. A hierarchical pyramidal decomposition with maximal decimation is used. For one level of decomposition, the input image I is partitioned into two subimages I/sub 1/ and I/sub 2/ obtained by downsampling. The subimage I/sub 1/ is unchanged. The subimage I/sub 2/ is replaced by the rounded output I/sub h/ of a 2D FIR filter whose coefficients have first been adapted to I and which has the entries I/sub 1/ and I/sub 2/. A similar processing is then applied one time to each of the subimages I/sub 1/ and I/sub 2/. The nonlinearity introduced by the rounding permits us to perfectly inverse the process, even when inverse filters (which are all ARMA) are not BIBO stable. Applications are given in lossless image coding, with possibility of embedded zerotree coding.