spyrit.core.meas.FreeformLinearSplit.adjoint_H

FreeformLinearSplit.adjoint_H(m: tensor, unvectorize=False)

Apply adjoint of matrix H.

It computes

\[x = H^Tm,\]

where \(H \in \mathbb{R}^{M\times N}\) is the acquisition matrix (that may contain negative values), \(m \in \mathbb{R}^M\) is a measurement vector.

Note

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

Args:

m (torch.tensor): Measurements \(m\) whose dimensions self.meas_dims must have shape self.meas_shape.

Returns:

A batch of signals \(x\). If unvectorize is False, \(x\) has shape \((*, N)\) where \(*\) is the same as for m. If unvectorize is True, \(x\) is reshaped such that the dimensions self.meas_dims have shape self.meas_shape.

Examples:

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

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

Example 2: 3 measurements of length 10 are measured with an acquisition matrix of shape (10, 60). This produces 3 signals of length 60.

>>> import spyrit.core.meas as meas
>>> H = torch.randn(10, 60)
>>> meas_op = meas.LinearSplit(H, meas_shape=(15, 4))
>>> m = torch.randn(3, 10)
>>> x = meas_op.adjoint_H(m)
>>> print(x.shape)
torch.Size([3, 60])

Using unvectorize=True produces 3 signals of length (15, 4)

>>> x = meas_op.adjoint_H(m, unvectorize=True)
>>> print(x.shape)
torch.Size([3, 15, 4])