= Poisson data fidelity
{c}
{title2=$\int[y\log(y/s)+s-y]$}
For positive observations $y$ and positive predicted intensities $s$, this is the <generalized Kullback–Leibler divergence> with observation in the first argument. Its scalar derivative in $s$ is $1-y/s$ and its second derivative is $y/s^2>0$. It differs from the divergence of a reconstructed density from a reference density by which argument is varied. A linear prediction $s=Kx$ gives derivative $K^*(1-y/(Kx))$ through the <adjoint operator>, on suitable admissible function spaces. This fidelity arises from the negative log likelihood of a <Poisson observation model>, after removal of terms depending only on observations.
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