Identification of image and blur parameters in frequency domain using the EM algorithm.

Area of Science:

• Image processing
• Signal processing
• Computational imaging

Background:

• Previous methods focused on semicausal autoregressive (AR) parameter identification for images with observation noise only.
• Accurate identification of both causal and semicausal AR parameters and blur parameters is crucial for image restoration.

Purpose of the Study:

• To propose a novel approach for identifying causal and semicausal AR parameters and blur parameters in degraded images.
• To achieve this without requiring prior knowledge of observation noise power or the point spread function (PSF).

Main Methods:

• Decomposition of the image into 1-D independent complex scalar subsystems using the unitary discrete Fourier transform (DFT).
• Application of the expectation-maximization (EM) algorithm to each subsystem for identifying AR model and blur parameters of the transformed image.
• Utilizing the least squares (LS) method to identify the AR parameters of the original image.

Main Results:

• Successfully identified both causal and semicausal AR parameters and blur parameters.
• The expectation-maximization (EM) algorithm yielded the restored image as a byproduct.
• The proposed method does not require prior knowledge of noise variance or the point spread function (PSF).

Conclusions:

• The developed method effectively identifies AR and blur parameters for degraded images.
• This approach offers robust image restoration by overcoming limitations of previous methods.
• The technique provides a significant advancement in blind image deconvolution and parameter estimation.