pytomography.priors
#
This module contains classes/functionality for encorporating priors in statistical reconstruction algorithms. Under the modification \(L(\tilde{f}, f) \to L(\tilde{f}, f)e^{-\beta V(f)}\), the log-liklihood becomes \(\ln L(\tilde{f},f) - \beta V(f)\). Typically, the prior has a form \(V(f) = \sum_{r,s} w_{r,s} \phi(f_r,f_s)\). In this expression, \(r\) represents a voxel in the object, \(s\) represents a voxel nearby to voxel \(r\), and \(w_{r,s}\) represents a weighting between the voxels.
Submodules#
Package Contents#
Classes#
Abstract class for implementation of prior \(V(f)\) where \(V\) is from the log-posterior probability \(\ln L(\tilde{f}, f) - \beta V(f)\). Any function inheriting from this class should implement a |
|
Implementation of priors where gradients depend on summation over nearest neighbours \(s\) to voxel \(r\) given by : \(\frac{\partial V}{\partial f_r}=\beta\sum_{r,s}w_{r,s}\phi(f_r, f_s)\) where \(V\) is from the log-posterior probability \(\ln L (\tilde{f}, f) - \beta V(f)\). |
|
Subclass of |
|
Subclass of |
|
Subclass of |
|
Abstract class for assigning weight \(w_{r,s}\) in nearest neighbour priors. |
|
Implementation of |
|
Implementation of |
|
Implementation of |
- class pytomography.priors.Prior(beta)[source]#
Abstract class for implementation of prior \(V(f)\) where \(V\) is from the log-posterior probability \(\ln L(\tilde{f}, f) - \beta V(f)\). Any function inheriting from this class should implement a
foward
method that computes the tensor \(\frac{\partial V}{\partial f_r}\) where \(f\) is an object tensor.- Parameters:
beta (float) – Used to scale the weight of the prior
- set_object_meta(object_meta)#
Sets object metadata parameters.
- Parameters:
object_meta (ObjectMeta) – Object metadata describing the system.
- Return type:
None
- set_beta_scale(factor)#
Sets a scale factor for \(\beta\) required for OSEM when finite subsets are used per iteration.
- Parameters:
factor (float) – Value by which to scale \(\beta\)
- Return type:
None
- set_object(object)#
Sets the object \(f_r\) used to compute \(\frac{\partial V}{\partial f_r}\)
- Parameters:
object (torch.tensor) – Tensor of size [batch_size, Lx, Ly, Lz] representing \(f_r\).
- Return type:
None
- abstract compute_gradient()#
Abstract method to compute the gradient of the prior based on the
self.object
attribute.
- class pytomography.priors.NearestNeighbourPrior(beta, phi, weight=None, **kwargs)[source]#
Bases:
pytomography.priors.prior.Prior
Implementation of priors where gradients depend on summation over nearest neighbours \(s\) to voxel \(r\) given by : \(\frac{\partial V}{\partial f_r}=\beta\sum_{r,s}w_{r,s}\phi(f_r, f_s)\) 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. Input arguments should be \(f_r\), \(f_s\), and any kwargs passed to this initialization function.
weight (NeighbourWeight, optional) –
- set_object_meta(object_meta)#
Sets object metadata parameters.
- Parameters:
object_meta (ObjectMeta) – Object metadata describing the system.
- Return type:
None
- compute_gradient()#
Computes the gradient of 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.QuadraticPrior(beta, delta=1, weight=None)[source]#
Bases:
NearestNeighbourPrior
Subclass of
NearestNeighbourPrior
where \(\phi(f_r, f_s)= (f_r-f_s)/\delta\) corresponds to a quadratic prior \(V(f)=\frac{1}{4}\sum_{r,s} w_{r,s} \left(\frac{f_r-f_s}{\delta}\right)^2\)- Parameters:
beta (float) – Used to scale the weight of the prior
delta (float, optional) – Parameter \(\delta\) in equation above. Defaults to 1.
weight (NeighbourWeight, optional) –
- class pytomography.priors.LogCoshPrior(beta, delta=1, weight=None)[source]#
Bases:
NearestNeighbourPrior
Subclass of
NearestNeighbourPrior
where \(\phi(f_r,f_s)=\tanh((f_r-f_s)/\delta)\) corresponds to the logcosh prior \(V(f)=\sum_{r,s} w_{r,s} \log\cosh\left(\frac{f_r-f_s}{\delta}\right)\)- Parameters:
beta (float) – Used to scale the weight of the prior
delta (float, optional) – Parameter \(\delta\) in equation above. Defaults to 1.
weight (NeighbourWeight, optional) –
- class pytomography.priors.RelativeDifferencePrior(beta=1, gamma=1, weight=None)[source]#
Bases:
NearestNeighbourPrior
Subclass of
NearestNeighbourPrior
where \(\phi(f_r,f_s)=\frac{2(f_r-f_s)(\gamma|f_r-f_s|+3f_s + f_r)}{(\gamma|f_r-f_s|+f_r+f_s)^2}\) 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
gamma (float, optional) – Parameter \(\gamma\) in equation above. Defaults to 1.
weight (NeighbourWeight, optional) –
- class pytomography.priors.NeighbourWeight[source]#
Abstract class for assigning weight \(w_{r,s}\) in nearest neighbour priors.
- set_object_meta(object_meta)#
Sets object meta to get appropriate spacing information
- Parameters:
object_meta (ObjectMeta) – Object metadata.
- Return type:
None
- abstract __call__(coords)#
Computes the weight \(w_{r,s}\) given the relative position \(s\) of the nearest neighbour
- Parameters:
coords (Sequence[int,int,int]) – Tuple of coordinates
(i,j,k)
that represent the shift of neighbour \(s\) relative to \(r\).
- class pytomography.priors.EuclideanNeighbourWeight[source]#
Bases:
NeighbourWeight
Implementation of
NeighbourWeight
where inverse Euclidean distance is the weighting between nearest neighbours.- __call__(coords)#
Computes the weight \(w_{r,s}\) using inverse Euclidean distance between \(r\) and \(s\).
- Parameters:
coords (Sequence[int,int,int]) – Tuple of coordinates
(i,j,k)
that represent the shift of neighbour \(s\) relative to \(r\).
- class pytomography.priors.AnatomyNeighbourWeight(anatomy_image, similarity_function)[source]#
Bases:
NeighbourWeight
Implementation of
NeighbourWeight
where inverse Euclidean distance and anatomical similarity is used to compute neighbour weight.- Parameters:
anatomy_image (torch.Tensor[batch_size,Lx,Ly,Lz]) – Object corresponding to an anatomical image (such as CT/MRI)
similarity_function (Callable) – User-defined function that computes the similarity between \(r\) and \(s\) in the anatomical image. The function should be bounded between 0 and 1 where 1 represets complete similarity and 0 represents complete dissimilarity.
- set_object_meta(object_meta)#
Sets object meta to get appropriate spacing information
- Parameters:
object_meta (ObjectMeta) – Object metadata.
- __call__(coords)#
Computes the weight \(w_{r,s}\) using inverse Euclidean distance and anatomical similarity between \(r\) and \(s\).
- Parameters:
coords (Sequence[int,int,int]) – Tuple of coordinates
(i,j,k)
that represent the shift of neighbour \(s\) relative to \(r\).
- class pytomography.priors.TopNAnatomyNeighbourWeight(anatomy_image, N_neighbours)[source]#
Bases:
NeighbourWeight
Implementation of
NeighbourWeight
where inverse Euclidean distance and anatomical similarity is used. In this case, only the top N most similar neighbours are used as weight- Parameters:
anatomy_image (torch.Tensor[batch_size,Lx,Ly,Lz]) – Object corresponding to an anatomical image (such as CT/MRI)
N_neighbours (int) – Number of most similar neighbours to use
- set_object_meta(object_meta)#
Sets object meta to get appropriate spacing information
- Parameters:
object_meta (ObjectMeta) – Object metadata.
- compute_inclusion_tensor()#
- __call__(coords)#
Computes the weight \(w_{r,s}\) using inverse Euclidean distance and anatomical similarity between \(r\) and \(s\).
- Parameters:
coords (Sequence[int,int,int]) – Tuple of coordinates
(i,j,k)
that represent the shift of neighbour \(s\) relative to \(r\).