Integer Polar Coordinates for Compression

This paper introduces a family of integer-to-integer approximations to the Cartesian-to-polar coordinate transformation and analyzes its application to lossy compression. A high-rate analysis is provided for an encoder that first uniformly scalar quantizes, then transforms to "integer polar coordinates," and finally separately entropy codes angle and radius. For sources separable in polar coordinates, the performance (at high rate) is shown to match that of entropy-constrained unconstrained polar quantization - where the angular quantization is allowed to depend on the radius. Thus, for sources separable in polar coordinates but not separable in rectangular coordinates - including certain Gaussian scale mixtures - the proposed system performs better than any transform code. Furthermore, unlike unconstrained polar quantization, integer polar coordinates are appropriate for lossless compression of integer-valued vectors. Combination of integer polar coordinates with integer-to-integer transform coding is also discussed.