# LogPoissonLikelihood

### *class* deepinv.optim.LogPoissonLikelihood(N0=1024.0, mu=1 / 50.0)

Bases: [`DataFidelity`](https://deepinv.org/api/stubs/deepinv.optim.DataFidelity.html.md#deepinv.optim.DataFidelity)

Log-Poisson negative log-likelihood.

$$
\datafid{z}{y} =  N_0 (1^{\top} \exp(-\mu z)+ \mu \exp(-\mu y)^{\top}x)
$$

Corresponds to [`deepinv.physics.LogPoissonNoise`](https://deepinv.org/api/stubs/deepinv.physics.LogPoissonNoise.html.md#deepinv.physics.LogPoissonNoise) with the same arguments $N_0$ and $\mu$.
There is no closed-form of the proximal operator known.

* **Parameters:**
  * **N0** ([*float*](https://docs.python.org/3.12/library/functions.html#float)) – average number of photons
  * **mu** ([*float*](https://docs.python.org/3.12/library/functions.html#float)) – normalization constant

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## Examples using `LogPoissonLikelihood`:

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<!-- thumbnail-parent-div-open --><div class="sphx-glr-thumbcontainer" tooltip="This example shows how to use the Astra tomography toolbox with deepinv, a popular toolbox for tomography with GPU acceleration.">![](auto_examples/external-libraries/images/thumb/sphx_glr_demo_astra_tomography_thumb.png)

[Low-dose CT with ASTRA backend and Total-Variation (TV) prior](https://deepinv.org/auto_examples/external-libraries/demo_astra_tomography.html.md)

  <div class="sphx-glr-thumbnail-title">Low-dose CT with ASTRA backend and Total-Variation (TV) prior</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="In this example we use patch priors for limited angle computed tomography. More precisely, we consider the inverse problem y = \\mathrm{noisy}(Ax), where A is the discretized Radon transform with 100 equispace angles between 20 and 160 degrees. For the reconstruction, we minimize the variational problem">![](auto_examples/optimization/images/thumb/sphx_glr_demo_patch_priors_CT_thumb.png)

[Patch priors for limited-angle computed tomography](https://deepinv.org/auto_examples/optimization/demo_patch_priors_CT.html.md)

  <div class="sphx-glr-thumbnail-title">Patch priors for limited-angle computed tomography</div>
</div>
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