CompressedSensing

class deepinv.physics.CompressedSensing(m, img_size, channelwise=False, dtype=torch.float, device='cpu', rng=None, **kwargs)

Bases: LinearPhysics

Compressed Sensing forward operator. Creates a random sampling \(m \times n\) matrix where \(n\) is the number of elements of the signal, i.e., np.prod(img_size) and m is the number of measurements.

This class generates a random iid Gaussian matrix

\[A_{i,j} \sim \mathcal{N}(0,\frac{1}{m})\]

For image sizes bigger than 32 x 32, the forward computation can be prohibitively expensive due to its \(O(mn)\) complexity. In this case, we recommend using deepinv.physics.StructuredRandom instead.

An existing operator can be loaded from a saved .pth file via self.load_state_dict(save_path), in a similar fashion to torch.nn.Module.

Note

The forward operator has a norm which tends to \((1+\sqrt{n/m})^2\) for large \(n\) and \(m\) due to the Marcenko-Pastur law.

If dtype=torch.cfloat, the forward operator will be generated as a random i.i.d. complex Gaussian matrix

\[A_{i,j} \sim \mathcal{N} \left( 0, \frac{1}{2m} \right) + \mathrm{i} \mathcal{N} \left( 0, \frac{1}{2m} \right).\]

Parameters:

• m (int) – number of measurements.

• img_size (tuple) – shape (C, H, W) of inputs.

• channelwise (bool) – Channels are processed independently using the same random forward operator.

• dtype (torch.dtype) – Forward matrix is stored as a dtype. For complex matrices, use torch.cfloat. Default is torch.float.

• device (str) – Device to store the forward matrix.

• rng (torch.Generator) – (optional) a pseudorandom random number generator for the parameter generation. If None, the default Generator of PyTorch will be used.

---

Examples:

Compressed sensing operator with 100 measurements for a 3x3 image:

>>> from deepinv.physics import CompressedSensing
>>> seed = torch.manual_seed(0) # Random seed for reproducibility
>>> x = torch.randn(1, 1, 3, 3) # Define random 3x3 image
>>> physics = CompressedSensing(m=10, img_size=(1, 3, 3), rng=torch.Generator('cpu'))
>>> physics(x)
tensor([[-1.7769,  0.6160, -0.8181, -0.5282, -1.2197,  0.9332, -0.1668,  1.5779,
          0.6752, -1.5684]])

Examples using CompressedSensing:

Tour of forward sensing operators

Tour of forward sensing operators