State-Space Approach to Roundoff Error Analysis of Fractal Image Coding

Choong Ho LEE  Masayuki KAWAMATA  Tatsuo HIGUCHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.1   pp.159-165
Publication Date: 1997/01/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
fractal image coding,  iterated function systems,  roundoff error analysis,  state-space approach,  

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Roundoff error due to iterative computation with finite wordlength degrades the quality of decoded images in fractal image coding that employs a deterministic iterated function system. This paper presents a state-space approach to roundoff error analysis of fractal image coding for grey-scale images. The output noise variance matrix and the noise matrix are derived for the measures of error and the output noise variance is newly defined as the pixel mean of diagonal elements of the output noise matrix. A quantitative comparison of experimental roundoff error with analytical result is made for the output noise variance. The result shows that our analysis method is valid for the fractal image coding. Our analysis method is useful to design a real-time and low-cost decoding hardware with finite wordlength for fractal image coding.