SART_CUDA
=========

This is a GPU 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.

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 SART is used as the initial reconstruction.
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.
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
-------

.. tabs::
  .. group-tab:: Python
    .. code-block:: python

      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
      recon_id = astra.data2d.create('-vol', vol_geom, 0)
      cfg = astra.astra_dict('SART_CUDA')
      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)


  .. group-tab:: Matlab
    .. code-block:: matlab

	%% 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, 0);
	cfg = astra_struct('SART_CUDA');
	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_algorithm('delete', sart_id);

Extra features
--------------

SART_CUDA supports astra.algorithm.get_res_norm() / 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.)