Physics#

class deepinv.physics.Physics(A=lambda x, **kwargs: ..., noise_model=lambda x, **kwargs: ..., sensor_model=lambda x: ..., solver='gradient_descent', max_iter=50, tol=1e-4)[source]#

Bases: Module

Parent class for forward operators

It describes the general forward measurement process

\[y = N(A(x))\]

where \(x\) is an image of \(n\) pixels, \(y\) is the measurements of size \(m\), \(A:\xset\mapsto \yset\) is a deterministic mapping capturing the physics of the acquisition and \(N:\yset\mapsto \yset\) is a stochastic mapping which characterizes the noise affecting the measurements.

Parameters:

A (Callable) – forward operator function which maps an image to the observed measurements \(x\mapsto y\).
noise_model (deepinv.physics.NoiseModel, Callable) – function that adds noise to the measurements \(N(z)\). See the noise module for some predefined functions.
sensor_model (Callable) – function that incorporates any sensor non-linearities to the sensing process, such as quantization or saturation, defined as a function \(\eta(z)\), such that \(y=\eta\left(N(A(x))\right)\). By default, the sensor_model is set to the identity \(\eta(z)=z\).
max_iter (int) – If the operator does not have a closed form pseudoinverse, the gradient descent algorithm is used for computing it, and this parameter fixes the maximum number of gradient descent iterations.
tol (float) – If the operator does not have a closed form pseudoinverse, the gradient descent algorithm is used for computing it, and this parameter fixes the absolute tolerance of the gradient descent algorithm.
solver (str) – least squares solver to use. Only gradient descent is available for non-linear operators.

A(x, **kwargs)[source]#

Computes forward operator \(y = A(x)\) (without noise and/or sensor non-linearities)

Parameters:: x (torch.Tensor,list[torch.Tensor]) – signal/image
Returns:: (torch.Tensor) clean measurements

A_dagger(y, x_init=None)[source]#

Computes an inverse as:

\[x^* \in \underset{x}{\arg\min} \quad \|\forw{x}-y\|^2.\]

This function uses gradient descent to find the inverse. It can be overwritten by a more efficient pseudoinverse in cases where closed form formulas exist.

Parameters:

y (torch.Tensor) – a measurement \(y\) to reconstruct via the pseudoinverse.
x_init (torch.Tensor) – initial guess for the reconstruction.

Returns:

(torch.Tensor) The reconstructed image \(x\).

A_vjp(x, v)[source]#

Computes the product between a vector \(v\) and the Jacobian of the forward operator \(A\) evaluated at \(x\), defined as:

\[A_{vjp}(x, v) = \left. \frac{\partial A}{\partial x} \right|_x^\top v.\]

By default, the Jacobian is computed using automatic differentiation.

Parameters:

x (torch.Tensor) – signal/image.
v (torch.Tensor) – vector.

Returns:

(torch.Tensor) the VJP product between \(v\) and the Jacobian.

__mul__(other)[source]#

Concatenates two forward operators \(A = A_1\circ A_2\) via the mul operation

The resulting operator keeps the noise and sensor models of \(A_1\).

Parameters:: other (deepinv.physics.Physics) – Physics operator \(A_2\)
Returns:: (deepinv.physics.Physics) concatenated operator

forward(x, **kwargs)[source]#

Computes forward operator

\[y = N(A(x), \sigma)\]

Parameters:: x (torch.Tensor, list[torch.Tensor]) – signal/image
Returns:: (torch.Tensor) noisy measurements

noise(x, **kwargs)[source]#

Incorporates noise into the measurements \(\tilde{y} = N(y)\)

Parameters:

x (torch.Tensor) – clean measurements
noise_level (None, float) – optional noise level parameter

Returns:

noisy measurements

Return type:

Tensor

sensor(x)[source]#

Computes sensor non-linearities \(y = \eta(y)\)

Parameters:: x (torch.Tensor,list[torch.Tensor]) – signal/image
Returns:: (torch.Tensor) clean measurements

set_ls_solver(solver, max_iter=None, tol=None)[source]#

Change default solver for computing the least squares solution:

\[x^* \in \underset{x}{\arg\min} \quad \|\forw{x}-y\|^2.\]

Parameters:

solver (str) – solver to use. If the physics are non-linear, the only available solver is 'gradient_descent'. For linear operators, the options are 'CG', 'lsqr', 'BiCGStab' and 'minres' (see deepinv.optim.utils.least_squares() for more details).
max_iter (int) – maximum number of iterations for the solver.
tol (float) – relative tolerance for the solver, stopping when \(\|A(x) - y\| < \text{tol} \|y\|\).

set_noise_model(noise_model, **kwargs)[source]#

Sets the noise model

Parameters:: noise_model (Callable) – noise model

stack(other)[source]#

Stacks two forward operators \(A(x) = \begin{bmatrix} A_1(x) \\ A_2(x) \end{bmatrix}\)

The measurements produced by the resulting model are deepinv.utils.TensorList objects, where each entry corresponds to the measurements of the corresponding operator.

Returns a deepinv.physics.StackedPhysics object.

See Combining Physics for more information.