PiGDMDataFidelity#

class deepinv.sampling.PiGDMDataFidelity(denoiser=None, weight=1.0, clip=None, cg_max_iter=3, cg_tol=1e-4, verbose=False)[source]#

Bases: NoisyDataFidelity

Pseudoinverse-guided diffusion model (PiGDM) data-fidelity term.

This corresponds to the \(p(y|x_t)\) approximation proposed in [137]. For the VE parametrization \(x_t=x_0+\sigma_t\omega\), PiGDM uses the isotropic Gaussian approximation

\[p(x_0|x_t) \approx \mathcal{N} \left( x_0;D(x_t,\sigma_t),\Sigma_t(x_t) \right), \qquad \Sigma_t(x_t)=r_t^2\mathrm{Id}, \qquad r_t^2=\frac{\sigma_t^2}{1+\sigma_t^2}.\]

For a linear forward operator and Gaussian measurement noise with standard deviation \(\sigma_y\), integrating this approximation gives a Gaussian approximation of \(p_t(y|x_t)\). Its negative log-likelihood gradient is

\[-\nabla_{x_t} \log p_t(y|x_t) \approx \lambda J_D(x_t, \sigma_t)^\top A^\top \left(r_t^2 A A^\top + \sigma_y^2\mathrm{Id}\right)^{-1} \left(A D(x_t, \sigma_t) - y\right).\]

Here \(D\) is a denoiser and \(J_D\) is its Jacobian. The parameter \(\lambda\), exposed as weight, controls the scale of the data-fidelity term. The inverse is evaluated exactly for deepinv.physics.DecomposablePhysics operators and approximated with conjugate gradient for other linear operators. The measurement noise level \(\sigma_y\) is read from physics.noise_model.sigma.

Parameters:

  • denoiser (deepinv.models.Denoiser) – Denoiser network. It may be left as None when the data fidelity is passed to deepinv.sampling.PosteriorDiffusion, which supplies its denoiser.

  • weight (float) – Weighting factor \(\lambda\). Default: 1.0.

  • clip (tuple[float]) – If not None, clip the denoised output into [clip[0], clip[1]] interval. Default to None.

  • cg_max_iter (int) – Maximum number of conjugate-gradient iterations. Default: 3.

  • cg_tol (float) – Relative conjugate-gradient tolerance. Default: 1e-4.

  • verbose (bool) – If True, print conjugate-gradient convergence information. Default: False.

grad(x, y, physics, sigma, *args, get_model_outputs=False, **kwargs)[source]#

Compute the PiGDM data-fidelity gradient.

\[-\nabla_{x_t} \log p_t(y|x_t) \approx \lambda J_D(x_t, \sigma_t)^\top A^\top \left(r_t^2 A A^\top + \sigma_y^2\mathrm{Id}\right)^{-1} \left(A D(x_t, \sigma_t) - y\right).\]
Parameters:

  • x (torch.Tensor) – Current noisy iterate.

  • y (torch.Tensor) – Measurements.

  • physics (deepinv.physics.Physics) – Linear physics operator.

  • sigma (torch.Tensor, float) – Diffusion noise standard deviation.

  • get_model_outputs (bool) – If True, also return the denoised output along with the score. Default to False.

Returns:

PiGDM gradient, with the same shape and dtype as x.

Return type:

Tensor | tuple[Tensor, Tensor]

solve_inverse(physics, u, r_t2, sigma_y)[source]#

Apply \((r_t^2 A A^\top + \sigma_y^2\mathrm{Id})^{-1}\) to u.

Parameters:
Returns:

Solution in the measurement space.

Return type:

Tensor

Examples using PiGDMDataFidelity:#

Noisy data-fidelity terms for diffusion posterior sampling

Noisy data-fidelity terms for diffusion posterior sampling