Quantifying the benefits of positivity

Brandoch Calef

doi:10.1117/12.616585

23 August 2005 Quantifying the benefits of positivity

Brandoch Calef

Proceedings Volume 5896, Unconventional Imaging; 589605 (2005) https://doi.org/10.1117/12.616585
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

It is well known that positivity constraints improve the performance of image reconstruction procedures such as deconvolution. However, their impact on the recovered image is more difficult to characterize than linear constraints such as support. For the problem of deconvolution in the presence of additive Gaussian noise, we derive an approximation to the bias and variance of the maximum likelihood estimator and compare the improvement in mean-square error due to positivity with the gain derived from support constraints. Then we propose a generalized Bayes estimator and demonstrate that it has lower mean-square error in most cases than the maximum likelihood estimator. The degree to which it outperforms maximum likelihood is especially dramatic when SNR is low or blurring is strong.

Citation Download Citation

Brandoch Calef "Quantifying the benefits of positivity", Proc. SPIE 5896, Unconventional Imaging, 589605 (23 August 2005); https://doi.org/10.1117/12.616585

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