Embedded Polar Quantization

Embedded polar quantization can be useful for progressive transmission of circularly symmetric data, e.g., for fine-grain scalable coding of parametric audio. Sets of constrained-resolution embedded quantizers are built recursively by successive refinement processes, that are detailed for strict polar quantization and unrestricted polar quantization. The quadratic error minimization problem is solved using equations similar to those of Max, and the refinement algorithm can, in the unrestricted case, be simplified using a high-rate approximation. For Gaussian data, comparisons with reference non-embedded quantizers show that the embedding property comes at an often negligible cost in terms of rate-distortion performance.