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Improved Restoration of Noisy Images by Adaptive Least-Squares Post-Filtering

M. Unser

Signal Processing, vol. 20, no. 1, pp. 3-14, May 1990.



The author describes a class of post-filtering algorithms that adaptively compute a linear combination between a noisy image and a restored version of it obtained by linear filtering. A set of optimal weighting coefficients is derived by minimizing the quadratic error between the output of this system and a noise-free signal. The only a priori information that is required is the noise variance. The local application of this optimization principle leads to the definition of the constrained and nonconstrained adaptive least-squares filters (ACLSF and ALSF, respectively). These algorithms, and particularly the ACLSF, can be implemented in an extremely efficient way by using a fast recursive updating strategy. The author then considers the particular case of a moving average as the initial filter and compare this application of the ALSF and ACLSF with Lee's (1980) adaptive noise filtering algorithm. He also presents some simulations and experimental examples illustrating the capability of these algorithms to reduce noise efficiently while preserving image details.


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AUTHOR="Unser, M.",
TITLE="Improved Restoration of Noisy Images by Adaptive
        Least-Squares Post-Filtering",
JOURNAL="Signal Processing",
YEAR="1990",
volume="20",
number="1",
pages="3--14",
month="May",
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