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Causal and semicausal AR image model identification using the EM algorithm.

Y Yemez¹, E Anarim, Y Istefanopulos

¹Dept. of Electr. and Electron. Eng., Bogazici Univ., Istanbul.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 1, 1993

Summary

This study extends autoregressive (AR) parameter identification for noisy images. It proposes a novel method to identify both causal and semicausal AR parameters without prior noise knowledge, enhancing image restoration.

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Area of Science:

Digital Image Processing
Signal Processing
Statistical Modeling

Background:

Autoregressive (AR) parameter identification is crucial for image processing, especially for images degraded by observation noise.
Previous methods, like Katayama and Hirai (1990), focused on semicausal AR parameters.
A limitation of prior work was the requirement for a priori knowledge of observation noise power.

Purpose of the Study:

To extend existing methods for autoregressive (AR) parameter identification in noisy images.
To propose a novel approach for identifying both causal and semicausal AR parameters.
To achieve this without requiring prior knowledge of the observation noise power.

Main Methods:

Decomposition of the image into 1-D independent complex scalar subsystems using a vector state-space model and the unitary discrete Fourier transform (DFT).
Application of the expectation-maximization (EM) algorithm to each subsystem for identifying AR parameters of the transformed image.
Utilizing the least-square method to determine the AR parameters of the original image.

Main Results:

Successfully identified both causal and semicausal AR parameters of noisy images.
The expectation-maximization (EM) algorithm was effectively applied to transformed image subsystems.
The restored image was obtained as a direct byproduct of the parameter identification process.

Conclusions:

The proposed method effectively identifies causal and semicausal AR parameters in noisy images without prior noise power information.
The integration of DFT, state-space models, and the EM algorithm offers a robust approach to image parameter estimation.
This technique provides a pathway for improved image restoration by accurately estimating underlying image model parameters.