models/unrolled_dpir.py

import numpy as np
import deepinv
import torch
import deepinv as dinv
from deepinv.optim.data_fidelity import L2
from deepinv.optim.prior import PnP
from deepinv.unfolded import unfolded_builder
import copy
import deepinv.optim.utils

class PoissonGaussianDistance(dinv.optim.Distance):
    r"""
    Implementation of :math:`\distancename` as the normalized :math:`\ell_2` norm

    .. math::
        f(x) = (x-y)^{T}\Sigma_y(x-y)

    with :math:`\Sigma_y=\text{diag}(gamma y + \sigma^2)`

    :param float sigma: Gaussian noise parameter. Default: 1.
    :param float gain: Poisson noise parameter. Default 0.
    """

    def __init__(self, sigma=1.0, gain=0.):
        super().__init__()
        self.sigma = sigma
        self.gain = gain

    def fn(self, x, y, *args, **kwargs):
        r"""
        Computes the distance :math:`\distance{x}{y}` i.e.

        .. math::

            \distance{x}{y} = \frac{1}{2}\|x-y\|^2


        :param torch.Tensor u: Variable :math:`x` at which the data fidelity is computed.
        :param torch.Tensor y: Data :math:`y`.
        :return: (:class:`torch.Tensor`) data fidelity :math:`\datafid{u}{y}` of size `B` with `B` the size of the batch.
        """
        norm = 1.0 / (self.sigma**2 + y * self.gain)
        z = (x - y) * norm
        d = 0.5 * torch.norm(z.reshape(z.shape[0], -1), p=2, dim=-1) ** 2
        return d

    def grad(self, x, y, *args, **kwargs):
        r"""
        Computes the gradient of :math:`\distancename`, that is  :math:`\nabla_{x}\distance{x}{y}`, i.e.

        .. math::

            \nabla_{x}\distance{x}{y} = \frac{1}{\sigma^2} x-y


        :param torch.Tensor x: Variable :math:`x` at which the gradient is computed.
        :param torch.Tensor y: Observation :math:`y`.
        :return: (:class:`torch.Tensor`) gradient of the distance function :math:`\nabla_{x}\distance{x}{y}`.
        """
        norm = 1.0 / (self.sigma**2 + y * self.gain)
        return (x - y) * norm

    def prox(self, x, y, *args, gamma=1.0, **kwargs):
        r"""
        Proximal operator of :math:`\gamma \distance{x}{y} = \frac{\gamma}{2 \sigma^2} \|x-y\|^2`.

        Computes :math:`\operatorname{prox}_{\gamma \distancename}`, i.e.

        .. math::

           \operatorname{prox}_{\gamma \distancename} = \underset{u}{\text{argmin}} \frac{\gamma}{2\sigma^2}\|u-y\|_2^2+\frac{1}{2}\|u-x\|_2^2


        :param torch.Tensor x: Variable :math:`x` at which the proximity operator is computed.
        :param torch.Tensor y: Data :math:`y`.
        :param float gamma: thresholding parameter.
        :return: (:class:`torch.Tensor`) proximity operator :math:`\operatorname{prox}_{\gamma \distancename}(x)`.
        """
        norm = 1.0 / (self.sigma**2 + y * self.gain)
        return (x + norm * gamma * y) / (1 + gamma * norm)


class PoissonGaussianDataFidelity(dinv.optim.DataFidelity):
    r"""
    Implementation of the data-fidelity as the normalized :math:`\ell_2` norm

    .. math::

        f(x) = \|\forw{x}-y\|^2_{\text{diag}(\sigma^2 + y \gamma)}

    It can be used to define a log-likelihood function associated with Poisson Gaussian noise
    by setting an appropriate noise level :math:`\sigma`.

    :param float sigma: Standard deviation of the noise to be used as a normalisation factor.
    :param float gain: Gain factor of the data-fidelity term.
    """

    def __init__(self, sigma=1.0, gain=0.):
        super().__init__()
        self.d = PoissonGaussianDistance(sigma=sigma, gain=gain)
        self.gain = gain
        self.sigma = sigma

    def prox(self, x, y, physics, gamma=1.0, *args, **kwargs):
        r"""
        Proximal operator of :math:`\gamma \datafid{Ax}{y} = \frac{\gamma}{2\sigma^2}\|Ax-y\|^2`.

        Computes :math:`\operatorname{prox}_{\gamma \datafidname}`, i.e.

        .. math::

           \operatorname{prox}_{\gamma \datafidname} = \underset{u}{\text{argmin}} \frac{\gamma}{2\sigma^2}\|Au-y\|_2^2+\frac{1}{2}\|u-x\|_2^2


        :param torch.Tensor x: Variable :math:`x` at which the proximity operator is computed.
        :param torch.Tensor y: Data :math:`y`.
        :param deepinv.physics.Physics physics: physics model.
        :param float gamma: stepsize of the proximity operator.
        :return: (:class:`torch.Tensor`) proximity operator :math:`\operatorname{prox}_{\gamma \datafidname}(x)`.
        """
        assert isinstance(physics, dinv.physics.LinearPhysics), "not implemented for non-linear physics"   
        if isinstance(physics, dinv.physics.StackedPhysics):
            device=y[0].device
            noise_model = physics[-1].noise_model
        else:
            device=y.device
            noise_model = physics.noise_model
        if hasattr(noise_model, "gain"):
            self.gain = noise_model.gain.detach().to(device)
        if hasattr(noise_model, "sigma"):
            self.sigma = noise_model.sigma.detach().to(device)
        # Ensure sigma is a tensor and reshape if necessary
        if isinstance(self.sigma, float):
            self.sigma = torch.tensor([self.sigma], device=device)
        if self.sigma.ndim == 0 :
            self.sigma = self.sigma.unsqueeze(0).to(device)
        # Ensure gain is a tensor and reshape if necessary
        if isinstance(self.gain, float):
            self.gain = torch.tensor([self.gain], device=device)
        if self.gain.ndim == 0 :
            self.gain = self.gain.unsqueeze(0).to(device)
        if self.gain[0] > 0 :
            norm = gamma / (self.sigma[:, None, None, None]**2 + y * self.gain[:, None, None, None])
        else : 
            norm = gamma / (self.sigma[:, None, None, None]**2)
        A = lambda u: physics.A_adjoint(physics.A(u)*norm) + u
        b = physics.A_adjoint(norm*y) + x
        return deepinv.optim.utils.conjugate_gradient(A, b, init=x, max_iter=3, tol=1e-3)

from deepinv.optim.optim_iterators import OptimIterator, fStep, gStep

class myHQSIteration(OptimIterator):
    r"""
    Single iteration of half-quadratic splitting.

    Class for a single iteration of the Half-Quadratic Splitting (HQS) algorithm for minimising :math:`f(x) + \lambda \regname(x)`.
    The iteration is given by


    .. math::
        \begin{equation*}
        \begin{aligned}
        u_{k} &= \operatorname{prox}_{\gamma f}(x_k) \\
        x_{k+1} &= \operatorname{prox}_{\sigma \lambda \regname}(u_k).
        \end{aligned}
        \end{equation*}


    where :math:`\gamma` and :math:`\sigma` are step-sizes. Note that this algorithm does not converge to
    a minimizer of :math:`f(x) + \lambda  \regname(x)`, but instead to a minimizer of
    :math:`\gamma\, ^1f+\sigma \lambda \regname`, where :math:`^1f` denotes
    the Moreau envelope of :math:`f`

    """

    def __init__(self, **kwargs):
        super(myHQSIteration, self).__init__(**kwargs)
        self.g_step = mygStepHQS(**kwargs)
        self.f_step = myfStepHQS(**kwargs)
        self.requires_prox_g = True

class myfStepHQS(fStep):
    r"""
    HQS fStep module.
    """

    def __init__(self, **kwargs):
        super(myfStepHQS, self).__init__(**kwargs)

    def forward(self, x, cur_data_fidelity, cur_params, y, physics):
        r"""
        Single proximal step on the data-fidelity term :math:`f`.

        :param torch.Tensor x: Current iterate :math:`x_k`.
        :param deepinv.optim.DataFidelity cur_data_fidelity: Instance of the DataFidelity class defining the current data_fidelity.
        :param dict cur_params: Dictionary containing the current parameters of the algorithm.
        :param torch.Tensor y: Input data.
        :param deepinv.physics.Physics physics: Instance of the physics modeling the data-fidelity term.
        """
        return cur_data_fidelity.prox(x, y, physics, gamma=cur_params["stepsize"])

class mygStepHQS(gStep):
    r"""
    HQS gStep module.
    """

    def __init__(self, **kwargs):
        super(mygStepHQS, self).__init__(**kwargs)

    def forward(self, x, cur_prior, cur_params):
        r"""
        Single proximal step on the prior term :math:`\lambda \regname`.

        :param torch.Tensor x: Current iterate :math:`x_k`.
        :param dict cur_prior: Class containing the current prior.
        :param dict cur_params: Dictionary containing the current parameters of the algorithm.
        """
        return cur_prior.prox(
            x,
            sigma_denoiser = cur_params["g_param"],
            gain_denoiser = cur_params["gain_param"],
            gamma=cur_params["lambda"] * cur_params["stepsize"],
        )


def get_unrolled_architecture(gain_param_init = 1e-3, weight_tied = True, model = None, device = 'cpu'):

    # Unrolled optimization algorithm parameters
    max_iter = 8  # number of unfolded layers

    # Select the data fidelity term
    

    # Set up the trainable denoising prior
    # Here the prior model is common for all iterations
    if model is not None : 
        denoiser = model.to(device)
    else :
        denoiser = dinv.models.DRUNet(
        pretrained= '/lustre/fswork/projects/rech/nyd/commun/mterris/base_checkpoints/drunet_deepinv_color_finetune_22k.pth',
        ).to(device)

    class myPnP(PnP):
        r"""
        Gradient-Step Denoiser prior.
        """

        def __init__(self, *args, **kwargs):
            super().__init__(*args, **kwargs)

        def prox(self, x, sigma_denoiser, gain_denoiser, *args, **kwargs):
            if not self.training:
                pad = (-x.size(-2) % 8, -x.size(-1) % 8)
                x = torch.nn.functional.pad(x, (0, pad[1], 0, pad[0]), mode="constant")
            out = self.denoiser(x, sigma=sigma_denoiser, gamma=gain_denoiser)
            if not self.training:
                out = out[..., : -pad[0] or None, : -pad[1] or None]
            return out
    
    data_fidelity = PoissonGaussianDataFidelity()
    
    if not weight_tied :
        prior = [myPnP(denoiser=copy.deepcopy(denoiser)) for i in range(max_iter)]
    else :
        prior = [myPnP(denoiser=denoiser)]
    
    def get_DPIR_params(noise_level_img, max_iter=8):
        r"""
        Default parameters for the DPIR Plug-and-Play algorithm.

        :param float noise_level_img: Noise level of the input image.
        """
        s1 = 49.0 / 255.0
        s2 = noise_level_img
        sigma_denoiser = np.logspace(np.log10(s1), np.log10(s2), max_iter).astype(
            np.float32
        )
        stepsize = (sigma_denoiser / max(0.01, noise_level_img)) ** 2
        lamb = 1 / 0.23
        return list(sigma_denoiser), list(lamb * stepsize)

    sigma_denoiser, stepsize = get_DPIR_params(0.05)
    stepsize = torch.tensor(stepsize) * (torch.tensor(sigma_denoiser)**2)
    gain_denoiser = [gain_param_init]*len(sigma_denoiser)
    params_algo = {"stepsize": stepsize, "g_param": sigma_denoiser, "gain_param": gain_denoiser}

    trainable_params = [
        "g_param",
        "gain_param"
        "stepsize",
    ]  # define which parameters from 'params_algo' are trainable

    # Define the unfolded trainable model.
    model = unfolded_builder(
        iteration=myHQSIteration(),
        params_algo=params_algo.copy(),
        trainable_params=trainable_params,
        data_fidelity=data_fidelity,
        max_iter=max_iter,
        prior=prior,
        device=device,
    )

    return model.to(device)