Lagrangian global optimization of two-description scalar quantizers

We develop an efficient Lagrangian-type algorithm for optimal two-description fixed-rate scalar quantizer design, for a very large class of distortion measures. Our key result is the discovery that the Lagrangian multiplier for the globally optimal solution exists. Although Lagrangian optimization is a method of choice for quantizer design, none of the previous algorithms using this method was shown to guarantee the global optimality for any instance of the problem.