Note
Go to the end to download the full example code.
Deep Equilibrium (DEQ) algorithms for image deblurring#
This a toy example to show you how to use DEQ to solve a deblurring problem.
Note that this is a small dataset for training. For optimal results, use a larger dataset.
For visualizing the training, you can use Weight&Bias (wandb) by setting wandb_vis=True.
For now DEQ is only possible with PGD, HQS and GD optimization algorithms.
import deepinv as dinv
from pathlib import Path
import torch
from torch.utils.data import DataLoader
from deepinv.optim.data_fidelity import L2
from deepinv.optim.prior import PnP
from deepinv.unfolded import DEQ_builder
from torchvision import transforms
from deepinv.utils.demo import load_dataset, load_degradation
Setup paths for data loading and results.#
BASE_DIR = Path(".")
DATA_DIR = BASE_DIR / "measurements"
RESULTS_DIR = BASE_DIR / "results"
CKPT_DIR = BASE_DIR / "ckpts"
DEG_DIR = BASE_DIR / "degradations"
# Set the global random seed from pytorch to ensure reproducibility of the example.
torch.manual_seed(0)
device = dinv.utils.get_freer_gpu() if torch.cuda.is_available() else "cpu"
Load base image datasets and degradation operators.#
In this example, we use the CBSD500 dataset and the Set3C dataset for testing.
img_size = 32
n_channels = 3 # 3 for color images, 1 for gray-scale images
operation = "deblurring"
# For simplicity, we use a small dataset for training.
# To be replaced for optimal results. For example, you can use the larger "drunet" dataset.
train_dataset_name = "CBSD500"
test_dataset_name = "set3c"
# Generate training and evaluation datasets in HDF5 folders and load them.
test_transform = transforms.Compose(
[transforms.CenterCrop(img_size), transforms.ToTensor()]
)
train_transform = transforms.Compose(
[transforms.RandomCrop(img_size), transforms.ToTensor()]
)
train_base_dataset = load_dataset(train_dataset_name, transform=train_transform)
test_base_dataset = load_dataset(test_dataset_name, transform=test_transform)
Generate a dataset of low resolution images and load it.#
We use the Downsampling class from the physics module to generate a dataset of low resolution images.
# Use parallel dataloader if using a GPU to speed up training, otherwise, as all computes are on CPU, use synchronous
# dataloading.
num_workers = 4 if torch.cuda.is_available() else 0
# Degradation parameters
noise_level_img = 0.03
# Generate a motion blur operator.
kernel_index = 1 # which kernel to chose among the 8 motion kernels from 'Levin09.mat'
kernel_torch = load_degradation("Levin09.npy", DEG_DIR / "kernels", index=kernel_index)
kernel_torch = kernel_torch.unsqueeze(0).unsqueeze(
0
) # add batch and channel dimensions
# Generate the gaussian blur downsampling operator.
physics = dinv.physics.BlurFFT(
img_size=(n_channels, img_size, img_size),
filter=kernel_torch,
device=device,
noise_model=dinv.physics.GaussianNoise(sigma=noise_level_img),
)
my_dataset_name = "demo_DEQ"
n_images_max = (
1000 if torch.cuda.is_available() else 10
) # maximal number of images used for training
measurement_dir = DATA_DIR / train_dataset_name / operation
generated_datasets_path = dinv.datasets.generate_dataset(
train_dataset=train_base_dataset,
test_dataset=test_base_dataset,
physics=physics,
device=device,
save_dir=measurement_dir,
train_datapoints=n_images_max,
num_workers=num_workers,
dataset_filename=str(my_dataset_name),
)
train_dataset = dinv.datasets.HDF5Dataset(path=generated_datasets_path, train=True)
test_dataset = dinv.datasets.HDF5Dataset(path=generated_datasets_path, train=False)
Levin09.npy degradation downloaded in degradations/kernels
Dataset has been saved at measurements/CBSD500/deblurring/demo_DEQ0.h5
Define the DEQ algorithm.#
We use the helper function deepinv.unfolded.DEQ_builder() to defined the DEQ architecture.
The chosen algorithm is here HQS (Half Quadratic Splitting).
Note for DEQ, the prior and regularization parameters should be common for all iterations
to keep a constant fixed-point operator.
# Select the data fidelity term
data_fidelity = L2()
# Set up the trainable denoising prior. Here the prior model is common for all iterations. We use here a pretrained denoiser.
prior = PnP(denoiser=dinv.models.DnCNN(depth=20, pretrained="download").to(device))
# Unrolled optimization algorithm parameters
max_iter = 20 if torch.cuda.is_available() else 10
stepsize = [1.0] # stepsize of the algorithm
sigma_denoiser = [0.03] # noise level parameter of the denoiser
jacobian_free = False # does not perform Jacobian inversion.
params_algo = { # wrap all the restoration parameters in a 'params_algo' dictionary
"stepsize": stepsize,
"g_param": sigma_denoiser,
}
trainable_params = [
"stepsize",
"g_param",
] # define which parameters from 'params_algo' are trainable
# Define the unfolded trainable model.
model = DEQ_builder(
iteration="PGD", # For now DEQ is only possible with PGD, HQS and GD optimization algorithms.
params_algo=params_algo.copy(),
trainable_params=trainable_params,
data_fidelity=data_fidelity,
max_iter=max_iter,
prior=prior,
anderson_acceleration=True,
anderson_acceleration_backward=True,
history_size_backward=3,
history_size=3,
max_iter_backward=20,
jacobian_free=jacobian_free,
)
Define the training parameters.#
We use the Adam optimizer and the StepLR scheduler.
# training parameters
epochs = 10 if torch.cuda.is_available() else 2
learning_rate = 1e-4
train_batch_size = 32 if torch.cuda.is_available() else 1
test_batch_size = 3
# choose optimizer and scheduler
optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate, weight_decay=1e-8)
scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=int(epochs * 0.8))
# choose supervised training loss
losses = [dinv.loss.SupLoss(metric=dinv.metric.MSE())]
# Logging parameters
verbose = True
wandb_vis = False # plot curves and images in Weight&Bias
train_dataloader = DataLoader(
train_dataset, batch_size=train_batch_size, num_workers=num_workers, shuffle=True
)
test_dataloader = DataLoader(
test_dataset, batch_size=test_batch_size, num_workers=num_workers, shuffle=False
)
Train the network#
We train the network using the library’s train function.
trainer = dinv.Trainer(
model=model,
physics=physics,
epochs=epochs,
scheduler=scheduler,
device=device,
losses=losses,
optimizer=optimizer,
train_dataloader=train_dataloader,
eval_dataloader=test_dataloader,
save_path=str(CKPT_DIR / operation),
verbose=verbose,
show_progress_bar=True, # disable progress bar for better vis in sphinx gallery.
wandb_vis=wandb_vis, # training visualization can be done in Weight&Bias
)
trainer.train()
model = trainer.load_best_model() # load model with best validation PSNR
The model has 668229 trainable parameters
0%| | 0/10 [00:00<?, ?it/s]
Train epoch 1/2: 0%| | 0/10 [00:00<?, ?it/s]
Train epoch 1/2: 0%| | 0/10 [00:00<?, ?it/s, TotalLoss=0.000786, PSNR=31]
Train epoch 1/2: 10%|██████▊ | 1/10 [00:00<00:03, 2.62it/s, TotalLoss=0.000786, PSNR=31]
Train epoch 1/2: 10%|██████▊ | 1/10 [00:00<00:03, 2.62it/s, TotalLoss=0.000786, PSNR=31]
Train epoch 1/2: 10%|██████▌ | 1/10 [00:00<00:03, 2.62it/s, TotalLoss=0.000663, PSNR=31.9]
Train epoch 1/2: 20%|█████████████▏ | 2/10 [00:00<00:02, 2.69it/s, TotalLoss=0.000663, PSNR=31.9]
Train epoch 1/2: 20%|█████████████▏ | 2/10 [00:00<00:02, 2.69it/s, TotalLoss=0.000663, PSNR=31.9]
Train epoch 1/2: 20%|█████████████▏ | 2/10 [00:01<00:02, 2.69it/s, TotalLoss=0.000505, PSNR=33.7]
Train epoch 1/2: 30%|███████████████████▊ | 3/10 [00:01<00:02, 2.72it/s, TotalLoss=0.000505, PSNR=33.7]
Train epoch 1/2: 30%|███████████████████▊ | 3/10 [00:01<00:02, 2.72it/s, TotalLoss=0.000505, PSNR=33.7]
Train epoch 1/2: 30%|████████████████████▍ | 3/10 [00:01<00:02, 2.72it/s, TotalLoss=0.0033, PSNR=30.1]
Train epoch 1/2: 40%|███████████████████████████▏ | 4/10 [00:01<00:02, 2.70it/s, TotalLoss=0.0033, PSNR=30.1]
Train epoch 1/2: 40%|███████████████████████████▏ | 4/10 [00:01<00:02, 2.70it/s, TotalLoss=0.0033, PSNR=30.1]
Train epoch 1/2: 40%|██████████████████████████▊ | 4/10 [00:01<00:02, 2.70it/s, TotalLoss=0.00516, PSNR=27.9]
Train epoch 1/2: 50%|█████████████████████████████████▌ | 5/10 [00:01<00:01, 2.69it/s, TotalLoss=0.00516, PSNR=27.9]
Train epoch 1/2: 50%|█████████████████████████████████▌ | 5/10 [00:01<00:01, 2.69it/s, TotalLoss=0.00516, PSNR=27.9]
Train epoch 1/2: 50%|█████████████████████████████████▌ | 5/10 [00:02<00:01, 2.69it/s, TotalLoss=0.00446, PSNR=28.3]
Train epoch 1/2: 60%|████████████████████████████████████████▏ | 6/10 [00:02<00:01, 2.69it/s, TotalLoss=0.00446, PSNR=28.3]
Train epoch 1/2: 60%|████████████████████████████████████████▏ | 6/10 [00:02<00:01, 2.69it/s, TotalLoss=0.00446, PSNR=28.3]
Train epoch 1/2: 60%|████████████████████████████████████████▏ | 6/10 [00:02<00:01, 2.69it/s, TotalLoss=0.00451, PSNR=27.5]
Train epoch 1/2: 70%|██████████████████████████████████████████████▉ | 7/10 [00:02<00:01, 2.70it/s, TotalLoss=0.00451, PSNR=27.5]
Train epoch 1/2: 70%|██████████████████████████████████████████████▉ | 7/10 [00:02<00:01, 2.70it/s, TotalLoss=0.00451, PSNR=27.5]
Train epoch 1/2: 70%|██████████████████████████████████████████████▉ | 7/10 [00:02<00:01, 2.70it/s, TotalLoss=0.00549, PSNR=26.5]
Train epoch 1/2: 80%|█████████████████████████████████████████████████████▌ | 8/10 [00:02<00:00, 2.71it/s, TotalLoss=0.00549, PSNR=26.5]
Train epoch 1/2: 80%|█████████████████████████████████████████████████████▌ | 8/10 [00:02<00:00, 2.71it/s, TotalLoss=0.00549, PSNR=26.5]
Train epoch 1/2: 80%|█████████████████████████████████████████████████████▌ | 8/10 [00:03<00:00, 2.71it/s, TotalLoss=0.00523, PSNR=26.3]
Train epoch 1/2: 90%|████████████████████████████████████████████████████████████▎ | 9/10 [00:03<00:00, 2.70it/s, TotalLoss=0.00523, PSNR=26.3]
Train epoch 1/2: 90%|████████████████████████████████████████████████████████████▎ | 9/10 [00:03<00:00, 2.70it/s, TotalLoss=0.00523, PSNR=26.3]
Train epoch 1/2: 90%|████████████████████████████████████████████████████████████▎ | 9/10 [00:03<00:00, 2.70it/s, TotalLoss=0.00485, PSNR=26.5]
Train epoch 1/2: 100%|██████████████████████████████████████████████████████████████████| 10/10 [00:03<00:00, 2.71it/s, TotalLoss=0.00485, PSNR=26.5]
Train epoch 1/2: 100%|██████████████████████████████████████████████████████████████████| 10/10 [00:03<00:00, 2.70it/s, TotalLoss=0.00485, PSNR=26.5]
0%| | 0/1 [00:00<?, ?it/s]
Eval epoch 1/2: 0%| | 0/1 [00:00<?, ?it/s]
Eval epoch 1/2: 0%| | 0/1 [00:00<?, ?it/s, PSNR=21.2]
Eval epoch 1/2: 100%|████████████████████████████████████████████████████████████████████████████████████████| 1/1 [00:00<00:00, 3.04it/s, PSNR=21.2]
Eval epoch 1/2: 100%|████████████████████████████████████████████████████████████████████████████████████████| 1/1 [00:00<00:00, 3.04it/s, PSNR=21.2]
Best model saved at epoch 1
0%| | 0/10 [00:00<?, ?it/s]
Train epoch 2/2: 0%| | 0/10 [00:00<?, ?it/s]
Train epoch 2/2: 0%| | 0/10 [00:00<?, ?it/s, TotalLoss=0.0121, PSNR=19.2]
Train epoch 2/2: 10%|██████▊ | 1/10 [00:00<00:03, 2.75it/s, TotalLoss=0.0121, PSNR=19.2]
Train epoch 2/2: 10%|██████▊ | 1/10 [00:00<00:03, 2.75it/s, TotalLoss=0.0121, PSNR=19.2]
Train epoch 2/2: 10%|██████▋ | 1/10 [00:00<00:03, 2.75it/s, TotalLoss=0.00651, PSNR=24.9]
Train epoch 2/2: 20%|█████████████▍ | 2/10 [00:00<00:02, 2.71it/s, TotalLoss=0.00651, PSNR=24.9]
Train epoch 2/2: 20%|█████████████▍ | 2/10 [00:00<00:02, 2.71it/s, TotalLoss=0.00651, PSNR=24.9]
Train epoch 2/2: 20%|█████████████▍ | 2/10 [00:01<00:02, 2.71it/s, TotalLoss=0.00792, PSNR=23.1]
Train epoch 2/2: 30%|████████████████████ | 3/10 [00:01<00:02, 2.72it/s, TotalLoss=0.00792, PSNR=23.1]
Train epoch 2/2: 30%|████████████████████ | 3/10 [00:01<00:02, 2.72it/s, TotalLoss=0.00792, PSNR=23.1]
Train epoch 2/2: 30%|████████████████████▍ | 3/10 [00:01<00:02, 2.72it/s, TotalLoss=0.0061, PSNR=25.4]
Train epoch 2/2: 40%|███████████████████████████▏ | 4/10 [00:01<00:02, 2.73it/s, TotalLoss=0.0061, PSNR=25.4]
Train epoch 2/2: 40%|███████████████████████████▏ | 4/10 [00:01<00:02, 2.73it/s, TotalLoss=0.0061, PSNR=25.4]
Train epoch 2/2: 40%|██████████████████████████▊ | 4/10 [00:01<00:02, 2.73it/s, TotalLoss=0.00583, PSNR=24.9]
Train epoch 2/2: 50%|█████████████████████████████████▌ | 5/10 [00:01<00:01, 2.74it/s, TotalLoss=0.00583, PSNR=24.9]
Train epoch 2/2: 50%|█████████████████████████████████▌ | 5/10 [00:01<00:01, 2.74it/s, TotalLoss=0.00583, PSNR=24.9]
Train epoch 2/2: 50%|██████████████████████████████████▌ | 5/10 [00:02<00:01, 2.74it/s, TotalLoss=0.00684, PSNR=24]
Train epoch 2/2: 60%|█████████████████████████████████████████▍ | 6/10 [00:02<00:01, 2.75it/s, TotalLoss=0.00684, PSNR=24]
Train epoch 2/2: 60%|█████████████████████████████████████████▍ | 6/10 [00:02<00:01, 2.75it/s, TotalLoss=0.00684, PSNR=24]
Train epoch 2/2: 60%|████████████████████████████████████████▏ | 6/10 [00:02<00:01, 2.75it/s, TotalLoss=0.00601, PSNR=24.8]
Train epoch 2/2: 70%|██████████████████████████████████████████████▉ | 7/10 [00:02<00:01, 2.74it/s, TotalLoss=0.00601, PSNR=24.8]
Train epoch 2/2: 70%|██████████████████████████████████████████████▉ | 7/10 [00:02<00:01, 2.74it/s, TotalLoss=0.00601, PSNR=24.8]
Train epoch 2/2: 70%|██████████████████████████████████████████████▉ | 7/10 [00:02<00:01, 2.74it/s, TotalLoss=0.00562, PSNR=24.9]
Train epoch 2/2: 80%|█████████████████████████████████████████████████████▌ | 8/10 [00:02<00:00, 2.75it/s, TotalLoss=0.00562, PSNR=24.9]
Train epoch 2/2: 80%|█████████████████████████████████████████████████████▌ | 8/10 [00:02<00:00, 2.75it/s, TotalLoss=0.00562, PSNR=24.9]
Train epoch 2/2: 80%|█████████████████████████████████████████████████████▌ | 8/10 [00:03<00:00, 2.75it/s, TotalLoss=0.00518, PSNR=25.2]
Train epoch 2/2: 90%|████████████████████████████████████████████████████████████▎ | 9/10 [00:03<00:00, 2.74it/s, TotalLoss=0.00518, PSNR=25.2]
Train epoch 2/2: 90%|████████████████████████████████████████████████████████████▎ | 9/10 [00:03<00:00, 2.74it/s, TotalLoss=0.00518, PSNR=25.2]
Train epoch 2/2: 90%|████████████████████████████████████████████████████████████▎ | 9/10 [00:03<00:00, 2.74it/s, TotalLoss=0.00474, PSNR=25.8]
Train epoch 2/2: 100%|██████████████████████████████████████████████████████████████████| 10/10 [00:03<00:00, 2.72it/s, TotalLoss=0.00474, PSNR=25.8]
Train epoch 2/2: 100%|██████████████████████████████████████████████████████████████████| 10/10 [00:03<00:00, 2.73it/s, TotalLoss=0.00474, PSNR=25.8]
0%| | 0/1 [00:00<?, ?it/s]
Eval epoch 2/2: 0%| | 0/1 [00:00<?, ?it/s]
Eval epoch 2/2: 0%| | 0/1 [00:00<?, ?it/s, PSNR=21.4]
Eval epoch 2/2: 100%|████████████████████████████████████████████████████████████████████████████████████████| 1/1 [00:00<00:00, 3.00it/s, PSNR=21.4]
Eval epoch 2/2: 100%|████████████████████████████████████████████████████████████████████████████████████████| 1/1 [00:00<00:00, 3.00it/s, PSNR=21.4]
Best model saved at epoch 2
Test the network#
trainer.test(test_dataloader)
test_sample, _ = next(iter(test_dataloader))
model.eval()
test_sample = test_sample.to(device)
# Get the measurements and the ground truth
y = physics(test_sample)
with torch.no_grad():
rec = model(y, physics=physics)
backprojected = physics.A_adjoint(y)
dinv.utils.plot(
[backprojected, rec, test_sample],
titles=["Linear", "Reconstruction", "Ground truth"],
suptitle="Reconstruction results",
)
0%| | 0/1 [00:00<?, ?it/s]
Test: 0%| | 0/1 [00:00<?, ?it/s]
Test: 0%| | 0/1 [00:00<?, ?it/s, PSNR=21.4, PSNR no learning=17]
Test: 100%|█████████████████████████████████████████████████████████████████████████████| 1/1 [00:00<00:00, 3.02it/s, PSNR=21.4, PSNR no learning=17]
Test: 100%|█████████████████████████████████████████████████████████████████████████████| 1/1 [00:00<00:00, 3.02it/s, PSNR=21.4, PSNR no learning=17]
Test results:
PSNR no learning: 16.952 +- 0.651
PSNR: 21.353 +- 1.324
/home/runner/work/deepinv/deepinv/deepinv/utils/plotting.py:320: UserWarning: This figure was using a layout engine that is incompatible with subplots_adjust and/or tight_layout; not calling subplots_adjust.
fig.subplots_adjust(top=0.75)
Total running time of the script: (0 minutes 9.125 seconds)