Optimal Generalized Gaussian Scale Estimator with Applications to Lloyd-Max Quantization of Images

Music City Center 

The generalized Gaussian distribution (GGD) is a versatile parametric family extensively used in signal and image processing for its ability to model diverse data distributions. In image compression algorithms like JPEG, the distributions of discrete cosine transform coefficients for a broad range of images are often represented by the GGD, encompassing widely used distributions such as Laplace and Gaussian. While extensive research focuses on estimating the GGD's shape parameter, fewer studies have developed accurate and optimal approaches for estimating the scale parameter, which is critical for controlling distribution spread and compression performance. We propose a novel optimal estimator for the GGD scale parameter and derive its exact mean squared error (MSE). We show analytically that our estimator has a uniformly smaller MSE than that of the maximum likelihood estimator. When applied to Lloyd-Max quantization of real images, our estimator demonstrates excellent performance, balancing feature preservation, compression efficiency, and minimal distortion.

Optimal Scale Estimator

Generalized Gaussian Distribution

Maximum Likelihood Estimator

Mean Squared Error

Image Compression

Lloyd-Max Quantization 

Section on Statistics in Imaging