SART

This is a CPU implementation of the Simultaneous Algebraic Reconstruction Technique (SART) for 2D data sets. It takes projection data and an initial reconstruction as input, and returns the reconstruction after a specified number of SART iterations. Each iteration of SART consists of an FP and BP of one single projection direction. The order of the projections can be specified.

Supported geometries: parallel, parallel_vec, fanflat, fanflat_vec, matrix.

Configuration options

Name	Description
ProjectorId	Projector object ID.
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.ProjectionOrder	This specifies the order in which the projections are used. Possible values are: ‘random’ (default), ‘sequential’, and ‘custom’. If ‘custom’ is specified, the option.ProjectionOrderList is required.
option.ProjectionOrderList	Required if option.ProjectionOrder = ‘custom’, ignored otherwise. An 1D array containing the custom order in which the projections are used.
option.MinConstraint	If specified, all values below MinConstraint will be set to MinConstraint. This can, for example, be used to enforce non-negative reconstructions.
option.MaxConstraint	If specified, all values above MaxConstraint will be set to MaxConstraint.
option.SinogramMaskId	If specified, data object ID of a projection-data-sized volume to be used as a mask.
option.ReconstructionMaskId	If specified, data object ID of a volume-data-sized volume to be used as a mask.

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('linear', 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)
cfg = astra.astra_dict('SART')
cfg['ProjectorId'] = projector_id
cfg['ProjectionDataId'] = sinogram_id
cfg['ReconstructionDataId'] = recon_id
cfg['option'] = {'ProjectionOrder': 'custom'}
# Set projection order to 0, 5, 10, ..., 175, 1, 6, 11, ..., 176, 2, 7, ...
cfg['option']['ProjectionOrderList'] = np.concatenate([
    np.arange(0, 5, N_ANGLES),
    np.arange(1, 5, N_ANGLES),
    np.arange(2, 5, N_ANGLES),
    np.arange(3, 5, N_ANGLES),
    np.arange(4, 5, N_ANGLES)
])
algorithm_id = astra.algorithm.create(cfg)

astra.algorithm.run(algorithm_id, iterations=10 * N_ANGLES)

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('linear', 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);
cfg = astra_struct('SART');
cfg.ProjectorId = projector_id;
cfg.ProjectionDataId = sinogram_id;
cfg.ReconstructionDataId = recon_id;
cfg.option.ProjectionOrder = 'custom';
% Set projection order to 0, 5, 10, ..., 175, 1, 6, 11, ..., 176, 2, 7, ...
cfg.option.ProjectionOrderList = horzcat( ...
    1:5:N_ANGLES, ...
    2:5:N_ANGLES, ...
    3:5:N_ANGLES, ...
    4:5:N_ANGLES, ...
    5:5:N_ANGLES  ...
) - 1;
algorithm_id = astra_mex_algorithm('create', cfg);

astra_mex_algorithm('iterate', algorithm_id, 10 * N_ANGLES);

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);