A quasi-linear time design for a near optimal entropy-constrained scalar quantizer

Entropy-constrained scalar quantizers (ECSQ) with the mean-squared error (MSE) distortion measure are widely used in the field of image compression. The design is based on the iterative Lloyd clustering algorithm, which ensures only a locally optimum quantizer and is highly dependent on the training parameters. We propose an alternative quasi-linear time (in the number of training samples) design that guarantees a near globally optimal ECSQ and we provide the upper bound on the loss of optimality. Our simulations, using l.l.d. Gaussian samples and a set of aerial images, indicate that our algorithm leads to a better rate-distortion performance than the Lloyd algorithm with a comparable design complexity.