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Coding Algorithm for Grayscale Images – Design of Piecewise Uniform Quantizer with Golomb–Rice Code and Novel Analytical Model for Performance Analysis
Volume 28, Issue 4 (2017), pp. 703–724
Pub. online: 1 January 2017      Type: Research Article      Open accessOpen Access
Received
1 June 2016
Accepted
1 May 2017
Published
1 January 2017

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.

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Biographies

Simić Nikola
simicnikola90@gmail.com

N. Simić was born in Niš, Serbia, in 1990. He received the BS and MS degrees from the Faculty of Electronic Engineering, University of Niš, Serbia, in 2013 and 2014, respectively, and he was awarded as the best graduated student of his generation. He is currently a student of doctoral studies at the same faculty. His current research interests include image coding and intelligent watermarking. Mr. Simić has been a reviewer of Multimedia Systems International Journal. He is an author and co-author of about 20 papers (8 of them in peer-reviewed international journals).

Perić Zoran H.
zoran.peric@elfak.ni.ac.rs

Z.H. Perić was born in Niš, Serbia, in 1964. He received the BS, MS and PhD degrees from the Faculty of Electronic Engineering, University of Niš, Serbia, in 1989, 1994 and 1999, respectively. He is a full-time professor at Department of Telecommunications, Faculty of Electronic Engineering, University of Niš. His current research interests include the information theory and signal processing. He is an author and co-author of over 200 papers. Dr. Perić has been a reviewer in a number of journals, including IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing, IEEE Transactions on Communications, Compel, Informatica, Information Technology and Control, Expert Systems with Applications and Digital Signal Processing.

Savić Milan S.
malimuzicar@gmail.com

M.S. Savić was born in Vranje, Serbia, in 1984. He received the MSc and PhD degrees in computer science from the Faculty of Electronic Engineering, University of Niš, Serbia, in 2008 and 2012, respectively. Milan Savić was an assistant research professor at Mathematical Institute of Serbian Academy of Sciences and Arts and currently he is an assistant professor at Faculty of Natural Science and Mathematics, University of Pristina. His current research interests include source coding and quantization of speech signals and images. He is an author and co-author of about 25 papers (13 of them in peer-reviewed international journals). Dr. Savić is a member of the Editorial Board of Canadian Journal Computer and Information Sciences.


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© 2017 Vilnius University
Open access article under the CC BY license.

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

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