kernel2d#

Module Contents#

Classes#

Kernel2D

FunctionalKernel2D

NGonKernel2D

Attributes#

device

kernel2d.device[source]#
class kernel2d.Kernel2D(a_min, a_max)[source]#
Parameters:

  • a_min (float) –

  • a_max (float) –

normalization_constant(a)[source]#

Computes the normalization constant for the kernel at each source-detector distance a. This method should be implemented in the child class.

Parameters:

a (torch.Tensor[Ld]) – Source detector distances

Returns:

Normalization at each source-detector distance

Return type:

torch.Tensor[Ld]

__call__(yv, a)[source]#

Computes the kernel value at each point in the meshgrid defined by xv and yv for each source-detector distance a. This method should be implemented in the child class.

Parameters:

  • xv (torch.Tensor[Lx,Ly]) – Meshgrid x-coordinates

  • yv (torch.Tensor[Lx,Ly]) – Meshgrid y-coordinates

  • a (torch.Tensor[Ld]) – Source-detector distances

Returns:

Kernel values at each point in the meshgrid for each source-detector distance

Return type:

torch.Tensor[Ld,Lx,Ly]

class kernel2d.FunctionalKernel2D(kernel_fn, amplitude_fn, sigma_fn, amplitude_params, sigma_params, a_min=-torch.inf, a_max=torch.inf)[source]#

Bases: Kernel2D

Parameters:

  • kernel_fn (Callable) –

  • amplitude_fn (Callable) –

  • sigma_fn (Callable) –

  • amplitude_params (torch.Tensor) –

  • sigma_params (torch.Tensor) –

  • a_min (float) –

  • a_max (float) –

_compute_norm_via_integral()[source]#

Compute the normalization constant by integrating k(x,y) from -infinity to infinity. To do this, a variable transformation is used to convert the integral to a definite integral over the range [-pi/2, pi/2]. The definite integral is computed using the Simpson’s rule.

Return type:

None

normalization_constant(xv, yv, a)[source]#

Obtains the normalization constant for the 2D kernel

Parameters:

  • xv (torch.Tensor[Lx,Ly]) – Meshgrid x-coordinates

  • yv (torch.Tensor[Lx,Ly]) – Meshgrid y-coordinates

  • a (torch.Tensor[Ld]) – Source-detector distances

Returns:

Normalization constant at each source-detector distance

Return type:

torch.Tensor[Ld]

__call__(xv, yv, a, normalize=False)[source]#

Computes the kernel at each source detector distance

Parameters:

  • xv (torch.Tensor[Lx,Ly]) – Meshgrid x-coordinates

  • yv (torch.Tensor[Lx,Ly]) – Meshgrid y-coordinates

  • a (torch.Tensor[Ld]) – Source-detector distances

  • normalize (bool, optional) – Whether or not to normalize the output of the kernel. Defaults to False.

Returns:

Kernel at each source-detector distance

Return type:

torch.Tensor[Ld,Lx,Ly]

class kernel2d.NGonKernel2D(N_sides, Nx, collimator_width, amplitude_fn, sigma_fn, amplitude_params, sigma_params, a_min=-torch.inf, a_max=torch.inf, rot=0)[source]#

Bases: Kernel2D

Parameters:

  • N_sides (int) –

  • Nx (int) –

  • collimator_width (float) –

  • amplitude_fn (Callable) –

  • sigma_fn (Callable) –

  • amplitude_params (torch.Tensor) –

  • sigma_params (torch.Tensor) –

  • rot (float) –

_compute_convolved_polygon()[source]#

Computes the convolved polygon

normalization_constant(xv, yv, a)[source]#

Computes the normalization constant for the kernel at each source-detector distance a.

Parameters:

  • xv (torch.Tensor[Lx,Ly]) – Meshgrid x-coordinates

  • yv (torch.Tensor[Lx,Ly]) – Meshgrid y-coordinates

  • a (torch.Tensor[Ld]) – Source-detector distances

Returns:

Normalization constant at each source detector distance.

Return type:

torch.Tensor[Ld]

__call__(xv, yv, a, normalize=False)[source]#

Computes the kernel at each source detector distance

Parameters:

  • xv (torch.Tensor[Lx,Ly]) – Meshgrid x-coordinates

  • yv (torch.Tensor[Lx,Ly]) – Meshgrid y-coordinates

  • a (torch.Tensor[Ld]) – Source-detector distances

  • normalize (bool, optional) – Whether or not to normalize the output of the kernel. Defaults to False.

Returns:

Kernel at each source-detector distance

Return type:

torch.Tensor[Ld,Lx,Ly]