pytomography.priors.relative_difference#

Module Contents#

Classes#

DiffAndSumSmoothnessPrior

Implementation of priors where gradients depend on difference and the sum of neighbouring voxels: \(\frac{\partial V}{\partial f_r}=\beta\sum_{r,s}w_{r,s}\phi(f_r-f_s, f_r+f_s)\) where \(V\) is from the log-posterior probability \(\ln L (\tilde{f}, f) - \beta V(f)\).

RelativeDifferencePrior

Subclass of SmoothnessPrior where \(\phi(f_r-f_s,f_r+f_s) = \frac{4(f_r-f_s)(f_r+f_s)}{((f_r+f_s)+\gamma|f_r-f_s|)^2}\) corresponds to the Relative Difference Prior \(V(f) = \sum_{r,s} w_{r,s} \frac{(f_r-f_s)^2}{(f_r+f_s)+\gamma|f_r-f_s|}\)

class pytomography.priors.relative_difference.DiffAndSumSmoothnessPrior(beta, phi, device='cpu', **kwargs)#

Bases: pytomography.priors.prior.Prior

Implementation of priors where gradients depend on difference and the sum of neighbouring voxels: \(\frac{\partial V}{\partial f_r}=\beta\sum_{r,s}w_{r,s}\phi(f_r-f_s, f_r+f_s)\) where \(V\) is from the log-posterior probability \(\ln L (\tilde{f}, f) - \beta V(f)\).

Parameters:
  • beta (float) – Used to scale the weight of the prior

  • phi (function) – Function $phi$ used in formula above

  • device (str, optional) – Pytorch device used for computation. Defaults to ‘cpu’.

get_kernel(sign=1)#

Obtains the kernel used to get \(\frac{\partial V}{\partial f_r}\) (this is an array with the same dimensions as the object space image)

Parameters:

sign (float) – Kernel computes image \(f_r + \text{sign} \cdot f_k\) for all 26 nearest neighbours \(k\) (i.e. a 3D image is returned with 26 channels). Defaults to 1.

Returns:

Kernel used for convolution (number of output channels equal to number of \(s\)), and array of weights \(w_s\) used in expression for gradient.

Return type:

(torch.nn.Conv3d, torch.tensor)

set_kernel(object_meta)#

Sets the kernel using get_kernel and the corresponding object metadata.

Parameters:

object_meta (ObjectMeta) – Metadata for object space.

Return type:

None

forward()#

Computes the prior on self.object

Returns:

Tensor of shape [batch_size, Lx, Ly, Lz] representing \(\frac{\partial V}{\partial f_r}\)

Return type:

torch.tensor

class pytomography.priors.relative_difference.RelativeDifferencePrior(beta=1, gamma=1, device='cpu')#

Bases: DiffAndSumSmoothnessPrior

Subclass of SmoothnessPrior where \(\phi(f_r-f_s,f_r+f_s) = \frac{4(f_r-f_s)(f_r+f_s)}{((f_r+f_s)+\gamma|f_r-f_s|)^2}\) corresponds to the Relative Difference Prior \(V(f) = \sum_{r,s} w_{r,s} \frac{(f_r-f_s)^2}{(f_r+f_s)+\gamma|f_r-f_s|}\)

Parameters:
  • beta (float) – Used to scale the weight of the prior

  • phi (function) – Function $phi$ used in formula above

  • gamma (float, optional) – Parameter $gamma$ in equation above. Defaults to 1.

  • device (str, optional) – Pytorch device used for computation. Defaults to ‘cpu’.

gradient(sum, diff, gamma, eps=1e-11)#

Gradient function.

Parameters:
  • sum (torch.Tensor) – tensor of size [batch_size,Lx,Ly,Lz] representing \(f_r+f_s\)

  • diff (torch.Tensor) – tensor of size [batch_size,Lx,Ly,Lz] representing \(f_r-f_s\)

  • gamma (torch.Tensor) – hyperparameter \(\gamma\)

  • eps (float, optional) – Used to prevent division by 0. Defaults to 1e-11.

Returns:

Returns \(\frac{(f_r-f_s)^2}{(f_r+f_s)+\gamma|f_r-f_s|}\) for a given \(r\) and \(s\).

Return type:

torch.Tensor