Analysis of scaling-factor-quantization error in fractal image coding

This paper proposes an analysis method of scaling-factor-quantization error in fractal image coding using a state-space approach with the statistical analysis method. It is shown that the statistical analysis method is appropriate and leads to a simple result, whereas the deterministic analysis method is not appropriate and leads to a complex result for the analysis of fractal image coding. We derive the output error variance matrix for the measure of error and define the output error variance by scalar quantity as the mean of diagonal elements of the output error variance matrix. Examples are given to show that the scaling-factor-quantization error due to iterative computation with finite-wordlength scaling factors degrades the quality of decoded images. A quantitative comparison of experimental scaling-factor-quantization error with analytical result is made for the output error variance. The result shows that our analysis method is valid for the fractal image coding.