Optimal Quantization Noise Allocation and Coding Gain in Transform Coding with Two-Dimensional Morphological Haar Wavelet

This paper analytically formulates both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform. The two-dimensional morphological Haar wavelet transform has been proposed as a nonlinear wavelet transform. It has been anticipated for application to nonlinear transform coding. To utilize a transformation to transform coding, both the optimal quantization noise allocation ratio and the coding gain of the transformation should be derived beforehand regardless of whether the transformation is linear or nonlinear. The derivation is crucial for progress of nonlinear transform image coding with nonlinear wavelet because the two-dimensional morphological Haar wavelet is the most basic nonlinear wavelet. We derive both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform by introducing appropriate approximations to handle the cumbersome nonlinear operator included in the transformation. Numerical experiments confirmed the validity of formulations. key words: coding gain, morphological Haar wavelet, nonlinear transform coding, nonlinear wavelet, optimal quantization noise allocation