**PURPOSE**- Calculates two sample reconstructions from randomly selected subsets containing half of the total projections and a a total-3D reconstruction from all the projections using conjugate gradients with regularization. This operation is the same as 'BP 3G' with the addition of the two randomly selected sample reconstructions. Only works for square projection images. See: Comparison of 'BP' operations. Example.

**SEE ALSO****BP CG**[Back Projection - 3D, Iterative, 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 3

- .TEMPLATE FOR IMAGE FILES: 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: ANGLES27

[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.].RECONSTRUCTED VOLUME FILE: VOL001

[Name of the output file.].FIRST SAMPLE VOLUME: VOL_1_001

[Name for the output volume calculated from a randomly selected set formed from half of the input projections.].SECOND SAMPLE VOLUME: VOL_2_001

[Name for the output volume calculated from remaining half of the input projections.].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.].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 1.0E-5, chi^2 limit to 0,
number of iterations to 20. If for a given data set
lambda was set correctly the procedure should converge
(error should become less than 1.0E-5) in approximately
15 steps. The procedures works properly if both relative
error and chi^2 error (difference) decrease steadily.
These values are printed out in the SPIDER results file).
- Assumes that projections are squares (NX = NY), so
the output volume has dimensions NX x NX x NX.
- This operation parallelized for use with MPI.
- Implemented by: Paul Penczek.
Fourier-based-spline Interpolation by G. Kishchenko.
- By using: 'BP CG 3L' this operation will request lists of sample images instead of creating random lists. This can be used to force same output over multiple trials. A similar effect can be accomplished with MD' using suboption 'SET SEED'

**SUBROUTINES**- BPCG, PREPCUB_S, HIANG, RPRQ, PRJCQ, aFBS3

**CALLER**- VTIL2

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