23 August 2005 Regularization for non-linear image restoration using a prior on the object power spectrum
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Abstract
Image restoration algorithms compensate for blur induced attenuation of frequency components that correspond to fine scale image features. However, for Fourier spatial frequency components with low signal to noise ratio, noise amplification outweighs the benefit of compensation and regularization methods are required. This paper investigates a generalization of the Wiener filter approach developed as a maximum a priori estimator based on statistical expectations of the object power spectrum. The estimate is also required to agree with physical properties of the system, specifically object positivity and Poisson noise statistics. These additional requirements preclude a closed form expression. Instead, the solution is determined by an iterative approach. Incorporation of the additional constraints results in significant improvement in the mean square error and in visual interpretability. Equally important, it is shown that the performance has weak sensitivity to the weight of the prior over a large range of SNR values, blur strengths, and object morphology, greatly facilitating practical use in an operational environment.
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David R. Gerwe, David R. Gerwe, Malani Jain, Malani Jain, Brandoch Calef, Brandoch Calef, Carlos Luna, Carlos Luna, } "Regularization for non-linear image restoration using a prior on the object power spectrum", Proc. SPIE 5896, Unconventional Imaging, 589604 (23 August 2005); doi: 10.1117/12.614451; https://doi.org/10.1117/12.614451
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