The minimum-average and minimum-maximum criteria in lossy compression

In this paper we propose an algorithm for the optimal bit allocation among dependent quantizers for the minimum-maximum (MINMAX) distortion criterion. We compare this algorithm to the well-known Lagrange multiplier method for the minimum-average (MINAVE) distortion criterion. We point out the differences between these two distortion criteria, and their implications for coding applications. We argue that even though the MINAVE criterion is more popular, in many cases, the MINMAX criterion is more appropriate. We introduce the algorithms for solving the optimal bit allocation problem among dependent quantizers for both criteria and highlight the similarities and differences. We present the two algorithms using the same frame-work, which sheds new light on the relationship between the MINAVE and the MINMAX criteria. We point out that any problem which can be solved with the MINAVE criterion can also be solved with the MINMAX criterion, since both approaches are based on the same assumptions.