Informatica

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.

This paper presents a model for signal compression, which consists of a piecewise uniform quantizer and a new lossless coder. The model is designed in a general manner, i.e. for any symmetrical signal distribution; this general theory is applied to design models for Gaussian and Laplacian distributions. Rigorous mathematical derivation of the expression for the bit-rate is presented. Forward adaptation of the model is done for non-stationary signals. Theory is proved by simulations in MATLAB and by an experiment with a real speech signal. The most important advantages of the model are low complexity and good performances – it satisfies G.712 standard for the speech transmission quality with 6.18 bps (bits per sample), which is significantly smaller than 8 bps required for quantizers used in PSTN (public switched telephone network) defined with G.711 standard.

In this paper, a piecewise uniform quantizer for input samples with discrete amplitudes for Laplacian source is designed and analyzed, and its forward adaptation is done. This type of quantizers is very often used in practice for the purpose of compression and coding of already quantized signals. It is shown that the design and the adaptation of quantizers for discrete input samples are different from the design and the adaptation of quantizers for continual input samples. A weighting function for PSQNR (peak signal-to-quantization noise ratio), which is obtained based on probability density function of variance of standard test images is introduced. Experiments are done, applying these quantizers for compression of grayscale images. Experimental results are very well matched to the theoretical results, proving the theory. Adaptive piecewise uniform quantizer designed for discrete input samples gives for 9 to 20 dB higher PSQNR compared to the fixed piecewise uniform quantizer designed for discrete input samples. Also it is shown that the adaptive piecewise uniform quantizer designed for discrete input samples gives higher PSQNR for 1.46 to 3.45 dB compared the adaptive piecewise uniform quantizer designed for continual input samples, which proves that the discrete model is more appropriate for image quantization than continual model.