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Iterative linear minimum mean-square-error image restoration from partially known blur
V Z Mesarović1, N P Galatsanos, M N Wernick
1Crystal Audio Products Division, Cirrus Logic Corporation, Austin, Texas 78744, USA.
Summary
This study introduces a new iterative algorithm for image restoration when blurring is uncertain. The method simultaneously restores images and estimates filter parameters, improving practical applications.
Area of Science:
- Image processing
- Signal processing
- Computational imaging
Background:
- Space-invariant image restoration is crucial but challenging when blurring is not precisely known.
- Existing methods often struggle with estimating parameters for restoration filters under such uncertainty.
Purpose of the Study:
- To develop a systematic approach for estimating restoration filter parameters in image restoration with unknown blurring.
- To propose an iterative algorithm that jointly restores images and estimates unknown blurring parameters.
Main Methods:
- Modeling the unknown point-spread function as a sum of deterministic and random components.
- Developing an expectation-maximization algorithm based on Gaussian statistical assumptions.
- Performing computations in the discrete Fourier transform domain for efficiency.
Main Results:
- An iterative expectation-maximization algorithm is derived for simultaneous image restoration and filter parameter estimation.
- Two algorithm versions are presented, based on different image statistical models.
- The algorithm demonstrates computational efficiency for large images due to its Fourier domain implementation.
Conclusions:
- The proposed iterative algorithm offers a systematic solution for image restoration with uncertain blurring.
- The method is computationally efficient and effective for practical image restoration tasks.
- Further evaluation of convergence properties and experimental performance is provided.