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	type	description
cfg.ProjectorId	required	The astra_mex_projector ID of the projector.
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 SART is used as the initial reconstruction.
cfg.option.SinogramMaskId	optional	If specified, the astra_mex_data2d ID of a projection-data-sized volume to be used as a mask.
cfg.option.ReconstructionMaskId	optional	If specified, the astra_mex_data2d ID of a volume-data-sized volume to be used as a mask.
cfg.option.MinConstraint	optional	If specified, all values below MinConstraint will be set to MinConstraint. This can, for example, be used to enforce non-negative reconstructions.
cfg.option.MaxConstraint	optional	If specified, all values above MaxConstraint will be set to MaxConstraint.
cfg.option.ProjectionOrder	optional	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.
cfg.option.ProjectionOrderList	optional	Required if option.ProjectionOrder = ‘custom’, ignored otherwise. A matlab vector containing the custom order in which the projections are used.

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('linear', 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
recon_id = astra.data2d.create('-vol', vol_geom, 0)
cfg = astra.astra_dict('SART')
cfg['ProjectorId'] = proj_id
cfg['ProjectionDataId'] = sinogram_id
cfg['ReconstructionDataId'] = recon_id
cfg['option'] = { }
cfg['option']['ProjectionOrder'] =  'custom'
# set projection order to 0, 5, 10, ..., 175, 1, 6, 11, ...., 176, 2, 7, .....
cfg['option']['ProjectionOrderList'] = numpy.array(range(180)).reshape(-1,5).T.reshape(-1)

sart_id = astra.algorithm.create(cfg)
astra.algorithm.run(sart_id, 10*180)
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(sart_id)

%% create phantom
V_exact = phantom(256);

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

%% create forward projection
[sinogram_id, sinogram] = astra_create_sino(V_exact, proj_id);

%% reconstruct
recon_id = astra_mex_data2d('create', '-vol', vol_geom, 0);
cfg = astra_struct('SART');
cfg.ProjectorId = proj_id;
cfg.ProjectionDataId = sinogram_id;
cfg.ReconstructionDataId = recon_id;
cfg.option.ProjectionOrder = 'custom';
cfg.option.ProjectionOrderList = [0:5:175 1:5:176 2:5:177 3:5:178 4:5:179];
sart_id = astra_mex_algorithm('create', cfg);
astra_mex_algorithm('iterate', sart_id, 10*180);
V = astra_mex_data2d('get', recon_id);
imshow(V, []);

%% garbage disposal
astra_mex_data2d('delete', sinogram_id, recon_id);
astra_mex_projector('delete', proj_id);
astra_mex_algorithm('delete', sart_id);

Further examples regarding the different projection orders can be found in example_sart_order.m .