#### NOTE
New to DeepInverse? Get started with the basics with the
[5 minute quickstart tutorial](https://deepinv.org/auto_examples/basics/demo_quickstart.html.md#sphx-glr-auto-examples-basics-demo-quickstart-py)..
# Expected Patch Log Likelihood (EPLL) for Denoising and Inpainting
In this example we use the expected patch log likelihood (EPLL) prior Zoran and Weiss[1](#footcite-zoran2011learning).
for denoising and inpainting of natural images.
To this end, we consider the inverse problem $y = Ax+\epsilon$, where $A$ is either the identity (for denoising)
or a masking operator (for inpainting) and $\epsilon\sim\mathcal{N}(0,\sigma^2 I)$ is white Gaussian noise with standard deviation $\sigma$.
```Python
import torch
import deepinv as dinv
from deepinv.optim import EPLL
from deepinv.physics import GaussianNoise, Denoising, Inpainting
from deepinv.loss.metric import PSNR
from deepinv.utils import plot
from deepinv.utils import load_example
device = dinv.utils.get_device()
```
```none
Selected GPU 0 with 29969.25 MiB free memory
```
## Load test image and model
As default EPLL loads pretrained weights for the Gaussian mixture model which where estimated based
on 50 mio patches extracted from the BSDS500 dataset. An example how to estimate the parameters of GMM
is included in the demo for limited-angle CT with patch priors.
```Python
test_img = load_example("CBSD_0010.png", grayscale=False).to(device)
patch_size = 6
model = EPLL(channels=test_img.shape[1], patch_size=patch_size, device=device)
```
## Denoising
In this setting, the operator $A$ is the identity; we set the noise level to $\sigma=25/255$.
Define noise model, operator and generate observation
```Python
sigma = 0.1
noise_model = GaussianNoise(sigma)
physics = Denoising(noise_model=noise_model)
observation = physics(test_img)
```
We use the default choice of the betas in the half quadratic splitting given by
$\beta \in \sigma^{-2} \{1,4,8,16,32\}$.
Generally, the betas are hyperparameters, which have to be chosen for each inverse problem separately.
```Python
# Reconstruction
with torch.no_grad():
x_out = model(observation, physics, batch_size=5000)
# PSNR computation and plots.
psnr_obs = PSNR()(observation, test_img).item()
psnr_recon = PSNR()(x_out, test_img).item()
print("PSNRs for Denoising:")
print("Observation: {0:.2f}".format(psnr_obs))
print("EPLL: {0:.2f}".format(psnr_recon))
plot(
[test_img, observation.clip(0, 1), x_out.clip(0, 1)],
["Ground truth", "Observation", "EPLL"],
)
```
```none
PSNRs for Denoising:
Observation: 20.00
EPLL: 28.68
```
## Inpainting
We now turn to a noisy inpainting problem, where the operator $A$ is a masking operator.
Define noise model, operator and generate observation
```Python
sigma = 0.01
physics = Inpainting(
img_size=test_img[0].shape,
mask=0.7,
device=device,
noise_model=GaussianNoise(sigma),
)
observation = physics(test_img)
```
Here, we need a different choice of beta. To this end, we extended the default choice
by two values and optimized a constant factor via grid search.
```Python
betas = [1.0, 5.0, 10.0, 40.0, 80.0, 160.0, 320.0]
# Reconstruction
with torch.no_grad():
x_out = model(observation, physics, betas=betas, batch_size=5000)
# PSNR computation and plots
psnr_obs = PSNR()(observation, test_img).item()
psnr_recon = PSNR()(x_out, test_img).item()
print("PSNRs for Inpainting:")
print("Observation: {0:.2f}".format(psnr_obs))
print("EPLL: {0:.2f}".format(psnr_recon))
plot(
[test_img, observation.clip(0, 1), x_out.clip(0, 1)],
["Ground truth", "Observation", "EPLL"],
)
```
```none
PSNRs for Inpainting:
Observation: 10.93
EPLL: 29.10
```
* **References:**
* Daniel Zoran and Yair Weiss. From learning models of natural image patches to whole image restoration. In *2011 international conference on computer vision*, 479–486. IEEE, 2011.
**Total running time of the script:** (0 minutes 2.284 seconds)
🏷 Tags: Denoising, Inpainting
[`Download Jupyter notebook: demo_epll.ipynb`](https://deepinv.org/auto_examples/optimization/_downloads/e199a1cb1899220da92fb0b6c5baae2d/demo_epll.ipynb)
[`Download Python source code: demo_epll.py`](https://deepinv.org/auto_examples/optimization/_downloads/1d063f1a961be328716be329132735d3/demo_epll.py)
[`Download zipped: demo_epll.zip`](https://deepinv.org/auto_examples/optimization/_downloads/e2aca9ff714612cdbd4610eed8152a19/demo_epll.zip)
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