FBP
===

This is a CPU implementation of the Filtered Backprojection (FBP) algorithm for 2D data sets. It takes a projector, projection data and an initial reconstruction as input, and returns the reconstruction.

Supported geometries: parallel.

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 data is overwritten.
========================	========	=============================================================================================

Example
-------

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

      import astra
      import scipy.io
      import matplotlib.pyplot as plt
      import numpy

      # Load phantom (from samples/python directory)
      V_exact = scipy.io.loadmat('phantom.mat')['phantom256']

      # 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)

      # 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('FBP')
      cfg['ProjectorId'] = proj_id
      cfg['ProjectionDataId'] = sinogram_id
      cfg['ReconstructionDataId'] = recon_id
      fbp_id = astra.algorithm.create(cfg)
      astra.algorithm.run(fbp_id)
      V = astra.data2d.get(recon_id)
      plt.gray()
      plt.imshow(V)
      plt.show()

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

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

      %% 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('FBP');
      cfg.ProjectorId = proj_id;
      cfg.ProjectionDataId = sinogram_id;
      cfg.ReconstructionDataId = recon_id;
      fbp_id = astra_mex_algorithm('create', cfg);
      astra_mex_algorithm('run', fbp_id);
      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', fbp_id);