= Proximal operator of Poisson data fidelity
{title2=$\operatorname{prox}_{\gamma E}(z)=(z-\gamma+\sqrt{(z-\gamma)^2+4\gamma y})/2$}
For $y>0$ and $\gamma>0$, minimizing $|x-z|^2/2+\gamma[y\log(y/x)+x-y]$ on $x>0$ gives $x^2+(\gamma-z)x-\gamma y=0$. The roots have opposite signs, so only the displayed positive root belongs to the effective domain. Strict positivity of the second derivative proves uniqueness. For an integral <Poisson data fidelity>, the <proximal operator> separates pointwise under the appropriate integrability assumptions.
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