Losses

Contains various loss functions to be used for optimization

It exposes three losses, one returning the mean squared amplitude error, one that returns the mean squared intensity error, and one that returns the maximum likelihood metric for a system with Poisson statistics.

cdtools.tools.losses.amplitude_mse(intensities, sim_intensities, mask=None)

Returns the mean squared error of a simulated dataset’s amplitudes

Calculates the mean squared error between a given set of measured diffraction intensities and a simulated set.

This function calculates the mean squared error between their associated amplitudes. Because this is not well defined for negative numbers, make sure that all the intensities are >0 before using this loss. Note that this is actually a sum-squared error, because this formulation makes it vastly simpler to compare error calculations between reconstructions with different minibatch size. I hope to find a better way to do this that is more honest with this cost function, though.

It can accept intensity and simulated intensity tensors of any shape as long as their shapes match, and the provided mask array can be broadcast correctly along them.

This is empirically the most useful loss function for most cases

Parameters:

  • intensities (torch.Tensor) – A tensor with measured detector values

  • sim_intensities (torch.Tensor) – A tensor of simulated detector intensities

  • mask (torch.Tensor) – A mask with ones for pixels to include and zeros for pixels to exclude

Returns:

loss – A single value for the mean amplitude mse

Return type:

torch.Tensor

cdtools.tools.losses.intensity_mse(intensities, sim_intensities, mask=None)

Returns the mean squared error of a simulated dataset’s intensities

Calculates the summed mean squared error between a given set of diffraction intensities - the measured set of detector intensities - and a simulated set of diffraction intensities. This function calculates the mean squared error between the intensities.

It can accept intensity and simulated intensity tensors of any shape as long as their shapes match, and the provided mask array can be broadcast correctly along them.

Parameters:

  • intensities (torch.Tensor) – A tensor with measured detector intensities.

  • sim_intensities (torch.Tensor) – A tensor of simulated detector intensities

  • mask (torch.Tensor) – A mask with ones for pixels to include and zeros for pixels to exclude

Returns:

loss – A single value for the mean intensity mse

Return type:

torch.Tensor

cdtools.tools.losses.poisson_nll(intensities, sim_intensities, mask=None, eps=1e-06, subtract_min=False)

Returns the Poisson negative log likelihood for simulated intensities

Calculates the overall Poisson maximum likelihood metric using diffraction intensities - the measured set of detector intensities - and a simulated set of intensities. This loss would be appropriate for detectors in a single-photon counting mode, with their output scaled to number of photons

Note that this calculation ignores the log(intensities!) term in the full expression for Poisson negative log likelihood. This term doesn’t change the calculated gradients so isn’t worth taking the time to compute

It can accept intensity and simulated intensity tensors of any shape as long as their shapes match, and the provided mask array can be broadcast correctly along them.

The default value of eps is 1e-6 - a nonzero value here helps avoid divergence of the log function near zero.

Parameters:

  • intensities (torch.Tensor) – A tensor with measured detector intensities.

  • sim_intensities (torch.Tensor) – A tensor of simulated detector intensities

  • mask (torch.Tensor) – A mask with ones for pixels to include and zeros for pixels to exclude

  • eps (float) – Optional, a small number to add to the simulated intensities

Returns:

loss – A single value for the poisson negative log likelihood

Return type:

torch.Tensor