Coding Algorithm for Grayscale Images – Design of Piecewise Uniform Quantizer with Golomb–Rice Code and Novel Analytical Model for Performance Analysis

Article type: Research Article

Authors: Simić, Nikola¹ | Perić, Zoran H.¹ | Savić, Milan S.^{2; *}

Affiliations: [1] Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia. E-mails: simicnikola90@gmail.com, zoran.peric@elfak.ni.ac.rs | [2] Faculty of Natural Science and Mathematics, University of Pristina, Ive Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia. E-mail: malimuzicar@gmail.com

Correspondence: [*] Corresponding author.

Abstract: Scalar quantizer selection for processing a signal with a unit variance is a difficult problem, while both selection and quantizer design for the range of variances is even tougher and to the authors’ best knowledge, it is not theoretically solved. Furthermore, performance estimation of various image processing algorithms is unjustifiably neglected and there are only a few analytical models that follow experimental analysis. In this paper, we analyse application of piecewise uniform quantizer with Golomb-Rice coding in modified block truncation coding algorithm for grayscale image compression, propose design improvements and provide a novel analytical model for performance analysis. Besides the nature of input signal, required compression rate and processing delay of the observed system have a strong influence on quantizer design. Consequently, the impact of quantizer range choice is analysed using a discrete designing variance and it was exploited to improve overall quantizer performance, whereas variable-length coding is applied in order to reduce quantizer’s fixed bit-rate. The analytical model for performance analysis is proposed by introducing Inverse Gaussian distribution and it is obtained by discussing a number of images, providing general closed-form solutions for peak-signal-to-noise ratio and the total average bit-rate estimation. The proposed quantizer design ensures better performance in comparison to the other similar methods for grayscale image compression, including linear prediction of pixel intensity and edge-based adaptation, whereas analytical model for performance analysis provides matching with the experimental results within the range of 1 dB for PSQNR and 0.2 bpp for the total average bit-rate.

Keywords: analytical model, Golomb–Rice coding, image compression, inverse Gaussian distribution, piecewise uniform quantizer, number of pixel change

Journal: Informatica, vol. 28, no. 4, pp. 703-724, 2017