DEAL#

class deepinv.models.DEAL(sigma_denoiser=0.1, lambda_reg=10.0, max_iter=50, auto_scale=False, target_y_std=25.0, color=False, device=None, clamp_output=True, pretrained='pretrained')[source]#

Bases: Reconstructor

Deep Equilibrium Attention Least Squares (DEAL) reconstruction model.

This model solves linear inverse problems using a learned equilibrium-based regularizer combined with iterative conjugate gradient least-squares updates. It can be used for image restoration and reconstruction tasks such as denoising, deblurring, and computed tomography reconstruction.

This implementation is adapted from the official DEAL repository.

For the original method, see Pourya et al.[1].

A pretrained network can be loaded by setting pretrained='download'.

The reconstruction is obtained by solving a regularized least-squares problem

\[\hat{x} = \arg\min_x \frac{1}{2}\|Ax - y\|^2 + \lambda g_\theta(x)\]

where \(A\) is the forward operator, \(y\) the measurements, and \(g_\theta\) is the learned adaptive regularizer.

In the implementation, the learned regularizer is induced by a masked linear operator of the form

\[L_{\theta,c}(u, x) = m_{\theta,c}(u) \odot K_{\theta,c} x,\]

so that the regularization term can be written as

\[g_{\theta}(u, x) = \sum_{c=1}^{C} \frac{1}{2}\|L_{\theta,c}(u, x)\|_2^2 = \sum_{c=1}^{C} \frac{1}{2}\|m_{\theta,c}(u) \odot K_{\theta,c} x\|_2^2,\]

where \(K_{\theta,c}\) are learned linear filters, \(m_{\theta,c}(u)\) are spatially varying masks predicted by the network, and \(\odot\) denotes element-wise multiplication.

The optimization is performed iteratively using a fixed-point scheme. At each outer iteration, the algorithm updates the reconstruction by solving a linearized least-squares subproblem using conjugate gradient:

\[x^{(k+1)} \approx \arg\min_x \frac{1}{2}\|Ax - y\|^2 + \frac{\lambda}{2} \sum_{c=1}^{C} \|m_{\theta,c}(x^{(k)}) \odot K_{\theta,c}x\|_2^2.\]
Parameters:

  • sigma_denoiser (float) – denoiser noise level parameter

  • lambda_reg (float) – regularization strength \(\lambda\) used by the DEAL solver

  • max_iter (int) – maximum number of outer fixed-point iterations

  • auto_scale (bool) – if True, rescales measurements in reconstruction mode when their empirical standard deviation is between 0 and 5. This option is useful when measurements are given in a normalized range but the pretrained DEAL inverse-problem solver expects a larger intensity scale. It is disabled by default.

  • target_y_std (float) – target measurement standard deviation used by auto_scale when enabled

  • color (bool) – if True, use the color DEAL variant; otherwise grayscale

  • device (str | None) – compute device. If None, use CUDA if available

  • clamp_output (bool) – if True, clamp output to [0, 1]

  • pretrained (str | None) – checkpoint path, 'download', 'pretrained', or None. If None, no pretrained weights are loaded. If 'download' or 'pretrained', the official DEAL pretrained weights are downloaded and loaded.

References:

property device: device#

Return the current device of the internal DEAL module.

forward(y, physics=None, sigma=None)[source]#

Run DEAL as either a denoiser or a reconstructor.

Parameters:

  • y (torch.Tensor) – input measurements

  • physics (LinearPhysics | None) – forward operator for reconstruction. If None, DEAL is applied as a denoiser.

  • sigma (float | None) – denoising noise level used when physics is None

Returns:

reconstructed or denoised image

Return type:

torch.Tensor

property mask: Tensor#

Return the current DEAL mask.

Examples using DEAL:#

DEAL denoising and reconstruction

DEAL denoising and reconstruction