spyrit.core.meas.LinearSplit.forward_H

LinearSplit.forward_H(x: tensor)

Simulate noisy measurements from matrix H.

It computes

\[m =\mathcal{N}\left(Hx\right),\]

where \(\mathcal{N} \colon\, \mathbb{R}^M \to \mathbb{R}^M\) represents a noise operator (e.g., Gaussian), \(H \in \mathbb{R}^{M\times N}\) is the acquisition matrix (that may contain negative values), \(x \in \mathbb{R}^N\) is the signal of interest, \(M\) is the number of DMD patterns, and \(N\) is the dimension of the signal.

Note

The acquisition matrix \(H\) is given by self.H.

Args:

x (torch.tensor): Signal \(x\) whose dimensions self.meas_dims must have shape shape self.meas_shape.

Returns:

torch.tensor: Measurement vector \(m\) of length self.M.

Examples:

Example 1: (3, 4) signals of length 15 are measured with an acquisition matrix of shape (10, 15). This produces (3, 4) measurements of length 10.

>>> import spyrit.core.meas as meas
>>> H = torch.randn(10, 15)
>>> meas_op = meas.LinearSplit(H)
>>> x = torch.randn(3, 4, 15)
>>> y = meas_op.forward_H(x)
>>> print(y.shape)
torch.Size([3, 4, 10])

Example 2: 3 signals of length (15, 4) are measured with an acquisition matrix of shape (10, 60). This produces 3 measurements of length 10. The acquisition matrix applies to both dimensions -2 and -1.

>>> import spyrit.core.meas as meas
>>> H = torch.randn(10, 60)
>>> meas_op = meas.LinearSplit(H, meas_shape=(15, 4))
>>> x = torch.randn(3, 15, 4)
>>> y = meas_op.forward_H(x)
>>> print(y.shape)
torch.Size([3, 10])
>>> print(meas_op.meas_dims)
torch.Size([-2, -1])