Rate Allocation in a Two Quantizer Coding System

The issue of backwards compatible image and video coding gained some attention in both MPEG and JPEG, let it be as extension for HEVC, let it be as the JPEG XT standardization initiative of the SC29WG1 committee. The coding systems work all on the principle of a base layer, perating in the low-dynamic range regime, using a one-mapped version of the HDR material as input, and an extension layer invisible to legacy applications. The extension layer allows implementations conforming to the full standard to reconstruct the original image in the high-dynamic range regime. What is also common to all approaches is the rate-allocation problem: How can one split the rate between base and extension layer to ensure optimal coding? In this work, an explicit answer is derived for a simplified model of a two-layer compression system in the high bit-rate approximation. For a HDR to LDR tone mapping that approximates the well-known sRGB non-linearity of gamma = 2.4 and a Laplacian probability density function, explicit results in the form of the Lambert-W-function are derived. The theoretical results are then verified in experiments using a JPEG XT demo implementation.