BP CG - Back Projection - 3D, Iterative, Conjugate Gradients ||*

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

1. 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.

2. 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).

3. Assumes that projections are squares (NX=NY), so the output volume has dimensions NX * NX * NX.

4. This operation parallelized for use with MPI.

5. Initially implemented by: Paul Penczek, Fourier-based-spline Interpolation by G. Kishchenko.

SUBROUTINES

BPCG, PREPCUB_S, HIANG, RPRQ, PRJCQ, FBS2, FBS3

CALLER

VTIL2