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	type	description
cfg.ProjectionDataId	required	The astra_mex_data2d ID of the projection data
cfg.ReconstructionDataId	required	The astra_mex_data2d ID of the reconstruction data. The content of this when starting SIRT is used as the initial reconstruction.
cfg.option.GPUindex	optional	Specifies which GPU to use. Default = 0.
cfg.option.DetectorSuperSampling	optional	Specifies the amount of detector supersampling, i.e. how many rays are cast per detector.
cfg.option.PixelSuperSampling	optional	Specifies the amount of pixel supersampling, i.e. how many (one dimension) subpixels are generated from a single parent pixel.

Example

import astra
import matplotlib.pyplot as plt
import numpy

# create geometries and projector
proj_geom = astra.create_proj_geom('parallel', 1.0, 256, numpy.linspace(0, numpy.pi, 180, endpoint=False))
vol_geom = astra.create_vol_geom(256,256)
proj_id = astra.create_projector('cuda', proj_geom, vol_geom)

# generate phantom image
V_exact_id, V_exact = astra.data2d.shepp_logan(vol_geom)

# create forward projection
sinogram_id, sinogram = astra.create_sino(V_exact, proj_id)

# reconstruct
# initialize with ones to allow for multiplicative updates
recon_id = astra.data2d.create('-vol', vol_geom, 1.0)
cfg = astra.astra_dict('EM_CUDA')
cfg['ProjectorId'] = proj_id
cfg['ProjectionDataId'] = sinogram_id
cfg['ReconstructionDataId'] = recon_id
em_id = astra.algorithm.create(cfg)
astra.algorithm.run(em_id, 15)
V = astra.data2d.get(recon_id)
plt.gray()
plt.imshow(V)
plt.show()

# garbage disposal
astra.data2d.delete([sinogram_id, recon_id, V_exact_id])
astra.projector.delete(proj_id)
astra.algorithm.delete(em_id)

%% create phantom
V_exact = phantom(256);

%% create geometries
proj_geom = astra_create_proj_geom('parallel', 1.0, 256, linspace2(0,pi,180));
vol_geom = astra_create_vol_geom(256,256);

%% create forward projection
[sinogram_id, sinogram] = astra_create_sino_cuda(V_exact, proj_geom, vol_geom);

%% reconstruct
recon_id = astra_mex_data2d('create', '-vol', vol_geom, 1.0);  % initialize with
% ones to allow for multiplicative updates
cfg = astra_struct('EM_CUDA');
cfg.ProjectionDataId = sinogram_id;
cfg.ReconstructionDataId = recon_id;
em_id = astra_mex_algorithm('create', cfg);
astra_mex_algorithm('iterate', em_id, 15);
V = astra_mex_data2d('get', recon_id);
imshow(V, []);

%% garbage disposal
astra_mex_data2d('delete', sinogram_id, recon_id);
astra_mex_algorithm('delete', em_id);

Extra features

EM_CUDA supports astra_mex_algorithm(‘get_res_norm’) to get the 2-norm of the difference between the projection data and the projection of the reconstruction. (The square root of the sum of squares of differences.)