Nonlinear transform coding: polar coordinates revisited

Summary form only given. We designed a family of integer-to-integer (i2i) approximations to the Cartesian-to-polar transformation and analyzed its behavior for high-rate transform coding. Denoting (ordinary, continuous) polar coordinates by (r, 0), our precise high-rate analysis relates the performance to the differential entropies of r² and 0, which are often easy to evaluate. One may thus predict when there is an improvement over linear transform coding. The analysis matches our simulations for coding of Gaussian scale mixtures and other polar-separable sources. The advantage over the best linear transform coder can be large. Our hope is to extend the polar-coordinate results to a general theory for nonlinear transform coding based on i2i implementations of arbitrary nonlinear transformations