EM_CUDA

This is a GPU implementation of the Expectation-Maximization (EM) algorithm for 2D data sets. It takes projection data and an initial reconstruction as input, and returns the reconstruction after a specified number of iterations.

Supported geometries: parallel, parallel_vec, fanflat, fanflat_vec.

Configuration options

Name	Description
ProjectionDataId	Projection data object ID.
ReconstructionDataId	ID of data object to store the result. The content of this data is used as the initial reconstruction.
option.DetectorSuperSampling	During forward projection, each detector element will be subdivided by this factor along each dimension. This should only be used if detector elements are larger than the pixels in the volume (default: 1).
option.PixelSuperSampling	During backprojection, each pixel in the volume will be subdivided by this factor along each dimension. This should only be used if pixels in the volume are larger than the detector elements (default: 1).
option.GPUindex	The index of the GPU to use (default: 0).

Example

import astra
import matplotlib.pyplot as plt
import numpy as np

# Create geometries and projector
N = 256
N_ANGLES = 180
det_spacing = 1.0
angles = np.linspace(0, np.pi, N_ANGLES)
proj_geom = astra.create_proj_geom('parallel', det_spacing, N, angles)
vol_geom = astra.create_vol_geom(N, N)
projector_id = astra.create_projector('cuda', proj_geom, vol_geom)

# Generate phantom image
phantom_id, phantom = astra.data2d.shepp_logan(vol_geom)

# Create forward projection
sinogram_id, sinogram = astra.create_sino(phantom_id, projector_id)

# Reconstruct
recon_id = astra.data2d.create('-vol', vol_geom, data=1.0)
cfg = astra.astra_dict('EM_CUDA')
cfg['ProjectionDataId'] = sinogram_id
cfg['ReconstructionDataId'] = recon_id
algorithm_id = astra.algorithm.create(cfg)

astra.algorithm.run(algorithm_id, iterations=100)

reconstruction = astra.data2d.get(recon_id)
plt.imshow(reconstruction, cmap='gray')

# Clean up
astra.data2d.delete([sinogram_id, recon_id, phantom_id])
astra.projector.delete(projector_id)
astra.algorithm.delete(algorithm_id)

%% Create phantom
N = 256;
phantom = phantom(N);

%% Create geometries and projector
det_spacing = 1.0;
N_ANGLES = 180;
angles = linspace(0, pi, N_ANGLES);
proj_geom = astra_create_proj_geom('parallel', det_spacing, N, angles);
vol_geom = astra_create_vol_geom(N, N);
projector_id = astra_create_projector('cuda', proj_geom, vol_geom);

%% Create forward projection
[sinogram_id, sinogram] = astra_create_sino(phantom, projector_id);

%% Reconstruct
recon_id = astra_mex_data2d('create', '-vol', vol_geom, 1.0);
cfg = astra_struct('EM_CUDA');
cfg.ProjectionDataId = sinogram_id;
cfg.ReconstructionDataId = recon_id;
algorithm_id = astra_mex_algorithm('create', cfg);

astra_mex_algorithm('iterate', algorithm_id, 100);

reconstruction = astra_mex_data2d('get', recon_id);
imshow(reconstruction, []);

%% Clean up
astra_mex_data2d('delete', sinogram_id, recon_id);
astra_mex_projector('delete', projector_id);
astra_mex_algorithm('delete', algorithm_id);

Extra features

EM_CUDA supports astra.algorithm.get_res_norm() / astra_mex_algorithm('get_res_norm') command to get the 2-norm of the residual for the reconstruction (the square root of the sum of squares of differences between the input and the projection of the result).