## Abstract

We demonstrate the use of image support constraints in a noise-reduction
algorithm. Previous work has revealed serious limits to the use of support if
image noise is wide-sense stationary in the frequency domain; we use simulation
and numerical calculations to show these limits are removed for nonstationary
noise generated by inverse-filtering adaptive optics image spectra. To quantify
the noise reduction, we plot fractional noise removed by the proposed algorithm
over a range of support sizes. We repeat this calculation for other noise
sources with varying degrees of stationarity.

© 1997 Optical Society of America

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### Equations (5)

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(1)
$${I}_{c}\left(\mathbf{u}\right)=\int d\mathbf{u}\phantom{\rule{.2em}{0ex}}I\left(v\right)W\left(\mathbf{u}-\mathbf{v}\right),$$
(2)
$$F(\mathbf{u},{u}_{c})=1-\frac{\mid \mathbf{u}\mid}{{u}_{c}},$$
(3)
$$\mathrm{PSD}{\left(\mathbf{u}\right)}_{R}=<{\mid \mathrm{Re}\left\{I\left(\mathbf{u}\right)\right\}-\mathrm{Re}\left\{\overline{I}\left(\mathbf{u}\right)\right\}\mid}^{2}>$$
(4)
$$\mathrm{PSD}{\left(\mathbf{u}\right)}_{I}=<{\mid \mathrm{Im}\left\{I\left(\mathbf{u}\right)\right\}-\mathrm{Im}\left\{\overline{I}\left(\mathbf{u}\right)\right\}\mid}^{2}>,$$
(5)
$${F}_{R\left(I\right)}=\frac{\int d\mathbf{u}\phantom{\rule{.2em}{0ex}}\left[\mathrm{PSD}{\left(\mathbf{u}\right)}_{R\left(I\right)}^{c}\right)-\mathrm{PSD}{\left(\mathbf{u}\right)}_{R\left(I\right)}^{u}]{\mid}_{>0}}{\int d\mathbf{u}\phantom{\rule{.2em}{0ex}}\mathrm{PSD}{\left(\mathbf{u}\right)}_{R\left(I\right)}^{u}},$$