spyrit.core.meas.DynamicLinear.forward

DynamicLinear.forward(x: tensor) → tensor

Simulates noisy dynamic measurements.

\[m = \mathcal{N}\left(\text{diag}(H x_{t=1, ..., M})\right),\]

where \(H \in \mathbb{R}^{M \times N}\) is the acquisition matrix, \(x_{t=1, ..., M} \in \mathbb{R}^{N \times M}\) is the temporal signal of interest, \(M\) is both the number of measurements and frames, \(N\) is the dimension of the signal in the field of view, and \(\text{diag}\colon\, \mathbb{R}^{M \times M} \to \mathbb{R}^M\) extracts the diagonal of its input.

Note

This method degrades measurements with noise. To compute \(Hx_{t=1, ..., M}\) only, see measure().

Args:

x (torch.tensor): A batch of temporal signals whose time dimension matches self.time_dim, and measured dimensions matches self.meas_dims.

Returns:

torch.tensor: A batch of measurement of shape \((*, M)\) where * denotes all the dimensions of the input tensor that are not included in self.meas_dims.

Example:

>>> import torch
>>> from spyrit.core.meas import DynamicLinear
>>> from spyrit.core.noise import Poisson
>>>
>>> x = torch.rand([1, 400, 3, 50, 50])  # dummy RGB video with 400 frames of size 50x50
>>> H = torch.rand([400, 40*40])  # dummy static measurement matrix
>>> alpha = 5  # noise level
>>> noise_op = Poisson(alpha=alpha, g=1/alpha)
>>> meas_op = DynamicLinear(H, time_dim=1, meas_shape=(40, 40), img_shape=(50, 50), noise_model=noise_op)
>>> print(meas_op)
DynamicLinear(
  (noise_model): Poisson()
)
>>>
>>> m = meas_op(x)  # simulate noisy dynamic measurements
>>> print(m.shape)
torch.Size([1, 3, 400])