spyrit.core.meas.Linear.adjoint

Linear.adjoint(m: tensor, unvectorize=False)[source]

Apply adjoint of matrix H.

It computes

\[x = H^Tm,\]

where \(H^T\in\mathbb{R}^{N\times M}\) is the adjoint of the acquisition matrix, \(m \in \mathbb{R}^M\) is a measurement.

Args:

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

unvectorize (bool, optional): Whether to unvectorize the measurement dimensions. This calls unvectorize() after mutiplication by the adjoint. Defaults to False.

Returns:

torch.tensor: 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 match the measurement shape self.meas_shape.

Example:

Example 2: (3, 4) measurements of length 10 produces (3, 4) signals of length 10.

>>> H = torch.randn(10, 15)
>>> meas_op = Linear(H)
>>> m = torch.randn(3, 4, 10)
>>> x = meas_op.adjoint(m)
>>> print(x.shape)
torch.Size([3, 4, 15])

Example 2: 3 measurements of length 10 produces 3 signals of length 60

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

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

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