====== Reconstruction ======
This logic is needed to create a 3D structure from 2D projections with assigned Euler angles. 

===== Usage =====
Reconstruction in Fourier space generally takes less time than in Real space and the output is mostly the same quality. 
It is highly recommended to use 'Reproject 3D parameter', as comparison of output projections to input classes is the best way of estimating the quality of the generated 3D model. 


===== Modes=====
==== Fourier ====
This mode makes reconstruction in Fourier space and is generally faster than Real space reconstruction

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^ Parameters                 ^ Description     ^
| Pixel in Angstrom  | Pixel size of the microscope |
| With gridding   | Use [[http://cds.ismrm.org/ismrm-1999/PDF3/664.PDF|gridding reconstruction algorithm]]  |
| Normalize 3D       | Normalizes the obtained 3D structure (mean=0)  |
| → 3D normalization sigma      | Sigma value for normalization |
| Padding factor   | Factor by which the box is padded with zeroes in fourier space |
| Already phase flipped       | Indicate whether phase flipping was applied on the previous steps |
| Reproject 3D   | Gives additional output of 2D reprojections of the obtained 3D structure |
| Symmetry  | Symmetry of the complex studied (if known) |
| With CTF      | Indicate whether header values with CTF parameters are available |

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^ Input   ^ Description ^
| Input  | Class averages with assigned angular info or alisums |

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^ Output   ^ Description ^
| 3D | 3D structure reconstructed from projections |
| Reprojections (if Reproject 3D parameter is enabled) | 2D projections obtained from 3D structure |


==== Real Space ====
This mode makes reconstruction in Real space 

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^ Parameters                 ^ Description     ^
| Normalize 3D       | Normalizes the obtained 3D structure (mean=0) |
| → 3D normalization sigma      | Sigma value for normalization |
| Reproject 3D   | Gives additional output of 2D reprojections of the obtained 3D structure |
| Symmetry  | Symmetry of the complex studied (if known) |

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^ Input   ^ Description ^
| Input  | Class averages with assigned angular info or alisums |

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^ Output   ^ Description ^
| 3D | 3D structure reconstructed from projections |
| Reprojections (if Reproject 3D parameter is enabled) | 2D projections obtained from 3D structure |

===== Concept =====
Real Space mode uses the [[http://www.owlnet.rice.edu/~elec539/Projects97/cult/node2.html|Filtered Back-Projection]] method, but applies 2D filtering instead of 1D, that reduces sensitivity to noise. 
Fourier Space Mode uses Fourier inversion method based on [[https://en.wikipedia.org/wiki/Projection-slice_theorem|central slice theorem]].
More information about the reconstruction in Real and Fourier space can be found in Chapter 7 of the following [[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3239172/pdf/cr100353t.pdf|review]].