BP CG - Back Projection - 3D, Conjugate gradients ||*

PURPOSE

Calculates 3D reconstruction using conjugate gradients with regularization.

SEE ALSO

BP 3D	[Back Projection - 3D, using Euler angles ||]
BP R2	[Back Projection - 2D, weighting of image series ||]
BP RP	[Back Projection - 3D, iterative, with constraints, ||*]
BP S2	[Back Projection - 2D, single tilt iterative, constrained ||]
BP W2	[Back Projection - 2D, filtered, weighted ||]

USAGE

.OPERATION: BP CG

.ENTER TEMPLATE FOR 2-D IMAGE FILE: PROJ***
[Enter template for projection input files.]

.ENTER FILE NUMBERS OR SELECTION DOC. FILE NAME: 1-700 OR IMAGES127
[Enter projection file numbers or the name of the document file containing projection file numbers in the first column.]

.RADIUS OF RESTORED 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 the name of the document file containing Eulerian angles for the projections used (psi, theta, phi).]

.DOES YOUR VOLUME HAVE SYMMETRIES? (Y/N): Y
[Not implemented yet.
Answer Yes if you want the symmetries to be internally enforced on your volume. The reconstruction in this case is calculated as though the projections were multiplied as many times as there are symmetries.]

If the answer was 'Y' SPIDER will ask:

.SYMMETRIES ANGLES DOC FILE: ANGSYM
[Enter the name of the document file containing Eulerian angles defining symmetries (psi, theta, phi). The angles should be such that when used in operation 'RT 3D' transform the volume into itself. The identity operation (angles 0,0,0) MUST be included.]

.RECONSTRUCTED 3-D FILE: VOLUME1001
[Name of the output file.]

.Error limit, Chi^2 limit: 1.0e-5,0.0
[Both value 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 correction limit is set to zero, this criterion is not used.]

.ITERATION LIMIT, MODE: 25,1
[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.

.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 detailes, but the process becomes more sensitive to noise.]

NOTES

1. The projections need not have power-of-2 dimensions.

2. If the radius of the reconstructed circle is too large comparing to the size of projections, a warning is printed. The reconstruction is calculated, but it is incorrect along the boundary.

3. Suggested lambda values for each mode:

    
                 mode         lambda 
                  1            2000 
                  2             500 
                  3             100 
   

   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 decrease steadily (printout is in the results file).

4. It is assumed that projections are squares (NSAM=NROW), so the output volume has dimensions NSAMxNSAMxNSAM.

5. Memory requirement: 2*(NSAM**3)

6. This operation parallelized for use with MPI.

7. Implemented by: Paul Penczek.

SUBROUTINES

REPCG, PREPCUB_S, HIANG, RPRQ, PRJCQ, BCKCQ

CALLER

VTIL2