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Update collections/_posts/2025-01-18-GradientStepDenoiser.md
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Co-authored-by: Nathan Painchaud <[email protected]>
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Tmodrzyk and nathanpainchaud authored Jan 23, 2025
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Expand Up @@ -133,7 +133,7 @@ These Plug-and-Play methods give very good reconstructions, with a natural robus

![Example of a PnP reconstruction](/collections/images/GradientStep/pnp.jpg)

However there are still several issues with these methods. With state-of-the-art denoisers, we have no theoretical guarantees that these schemes converge to a fix-point, let alone the minimum of our original optimization problem.
However there are still several issues with these methods. With state-of-the-art denoisers, we have no theoretical guarantees that these schemes converge to a fixed-point, let alone the minimum of our original optimization problem.

In order to have some theoretical guarantees, we need **a lot** of assumptions on $$D_\sigma$$, the most restrictive one is that $$D_\sigma$$ needs to be *contractive*, meaning that:

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