Physics#

class deepinv.physics.Physics(A=<function Physics.<lambda>>, noise_model=<function Physics.<lambda>>, sensor_model=<function Physics.<lambda>>, max_iter=50, tol=0.001)[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 (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.

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.

__add__(other)[source]#

Stacks two linear forward operators \(A(x) = \begin{bmatrix} A_1(x) \\ A_2(x) \end{bmatrix}\) via the add operation.

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