C. H. Lee. Quantization Error Analysis of Fractal Image Coding Based on State-Space Approach. Record Of Electrical And Communication Engineering Conversazione Tohoku University, 67(1):169-170, 1998.
This thesis models and analyzes the quantization error of fractal image coding using state-space approach and statistical analysis method. Two types of quantization errors are modeled and analyzed. One is roundoff error after multiplication and the other is coefficient-quantization error. Firstly, we model the roundoff error in the state space, and derive the output error variance matrix. We also define the output error variance by scalar quantity. The output error variance is described by three terms which depends on decimation ratio, coefficients, and wordlength. The method is experimentally verifed using a 32 x 32 Lena image. However, this method cannot be applied to large images, because the resultant wquation using this method is complex to compute due to the large-scale matrix computation. Secondly, using a simplified model for the roundoff error analysis, we obtain a simple resultant equation that does not need iterative computation for iteration number. The result is verified by testing on 12 standard images which have 256 x 256 sizes and 512 x 512 sizes. Lastly, we analyze the coefficient-quantization error using a simplified model and statistical method. The result obtained is verifield by testing on the 12 standard images used in the roundoff error analysis. This method gives a very simple equation for the output error variance of coefficient-quantization error.
@article{Lee98,
Author = {Lee, C. H.},
Title = {Quantization Error Analysis of Fractal Image Coding Based on State-Space Approach},
Journal = {Record Of Electrical And Communication Engineering Conversazione Tohoku University},
Volume = {67},
Number = {1},
Pages = {169--170},
Publisher = {Tohoku Daigaku Dentsu Danwakai},
Year = {1998}
}