spyrit.core.meas.HadamSplit2d.fast_pinv

HadamSplit2d.fast_pinv(m: tensor, vectorize=False) → tensor

Apply the pseudo inverse of H.

Args:

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

vectorize (bool): Whether to apply the vectorize() method after computation of the pseudo inverse.

Returns:

torch.tensor: Vectorized image \(x\) of length self.N.

Note

We use the separability of the 2D Hadamard transform. Only multiplications with the “1D” Hadamard matrix (i.e., self.H1d) are required. If the number of measurements is smaller than the number of pixels, the measurement vector is zero-padded.

Examples:

Example 1: No subsampling

>>> import torch
>>> import spyrit.core.meas as meas
>>> h = 32
>>> meas_op = meas.HadamSplit2d(h)
>>> m = torch.empty(10, h*h).uniform_(0, 1)
>>> x = meas_op.fast_pinv(m)
>>> print(x.shape)
torch.Size([10, 32, 32])

Example 2: With subsampling

>>> import torch
>>> import spyrit.core.meas as meas
>>> h, M = 32, 49
>>> meas_op = meas.HadamSplit2d(h, M)
>>> m = torch.empty(8, 2, M).uniform_(0, 1)
>>> x = meas_op.fast_pinv(m)
>>> print(x.shape)
torch.Size([8, 2, 32, 32])

Example 3: Output are vectors, not images

>>> import torch
>>> import spyrit.core.meas as meas
>>> h, M = 32, 49
>>> meas_op = meas.HadamSplit2d(h, M)
>>> m = torch.empty(8, 2, M).uniform_(0, 1)
>>> x = meas_op.fast_pinv(m, vectorize=True)
>>> print(x.shape)
torch.Size([8, 2, 1024])