**PURPOSE**- Calculates 3D reconstruction using conjugate gradients with regularization. Only works for square projection images. See: Comparison of 'BP' operations. Example.

**SEE ALSO****BP CG 3**[Back Projection - 3D, Iterative, sampled, Conjugate gradients ||*] **BP 3F**[Back Projection - 3D, Interpolated in Fourier space ||*] **BP 3D**[Back Projection - 3D, using Euler angles ||] **BP R2**[Back Projection - Weight image series ||] **BP RP**[Back Projection - 3D, iterative, Richardson, constrained ||*] **BP S2**[Back Projection - 2D, single tilt, iterative, constrained ||] **BP W2**[Back Projection - 2D, filtered, weighted ||]

**USAGE**- .OPERATION: BP CG

- .TEMPLATE FOR 2-D IMAGE FILE: PROJ***

[Enter template for projection input files.].FILE NUMBERS OR SELECTION DOC. FILE NAME: 1-700

[Enter projection file numbers or the name of the document file which contains the projection file numbers in its first register column.].RADIUS OF RECONSTRUCTED OBJECT: 23

[Enter radius of reconstructed object (smaller than half the volume size, see below for further restrictions). The reconstruction is calculated inside the sphere only.].ANGLES DOC FILE: ANGLESDOC

[Enter name of the document file which contains Eulerian angles: psi, theta, and phi in the first three registers columns. These angles specify the projection directions.].LINEAR OR FBS INTERPOLATION (L,F)? : F

[Use slower FBS Interpolation to get better resolution than the linear interpolated default operation. (The back-projection is then done using FBS interpolation however the projection steps continue to use bilinear interpolation.)].RECONSTRUCTED VOLUME FILE: VOL001

[Name of the output file.].ERROR LIMIT, CHI^2 LIMIT: 1.0E-5, 0.0

[Both values can be used as stopping criteria to terminate the iterations. When the relative error or chi-squared error of the structure becomes smaller than the preset value, the iterations are terminated. When error limit is set to zero, chi^2 limit is not used.

] If you are uncertain about selecting the limits, try: .00005, 0].ITERATION LIMIT, MODE: 20, 1

[Program will terminate after number of iterations given. Mode determines the regularization used:

0 - No regularization,

1 - First derivatives,

2 - Second derivatives,

3 - Third derivatives.

If you are uncertain about selecting number of iterations, try: 20 or 25.

If you are uncertain about selecting the mode, it does not seem to make much difference, try mode: 1].LAMBDA: 2000.

[Lambda determines relative weight of regularization. Large lambda results in a stronger supression of noise (thus smoother reconstruction), small lambda will give more details, but the process becomes more sensitive to noise. Suggested lambda values for each mode:Mode Lambda 1 2000 2 500 3 100

**NOTES**

- If the radius of the reconstructed circle is too large
compared to the size of projections, a warning is printed.
The reconstruction is calculated, but it is incorrect
along the boundary.
- Suggested values: Error limit should be set to 0.00005, chi^2 limit to 0, and
number of iterations to 20. For a given data set, if
lambda was set correctly, the procedure should converge
(error should become less than 1.0E-5) in approximately
15 steps. The procedure works properly if both relative
error and chi^2 error decrease steadily (See your
SPIDER results file).
- Assumes that projections are squares (NX=NY), so
the output volume has dimensions NX * NX * NX.
- This operation parallelized for use with MPI.
- Initially implemented by: Paul Penczek, Fourier-based-spline Interpolation by G. Kishchenko.

**SUBROUTINES**- BPCG, PREPCUB_S, HIANG, RPRQ, PRJCQ, FBS2, FBS3

**CALLER**- VTIL2

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