BP RP - Back Projection - 3D, iterative, with constraints, ||*

PURPOSE

Calculates 3D reconstruction using constraints.

SEE ALSO

BP 3F	[Back Projection - 3D, Interpolated in Fourier space ||*]
BP 32F	[Back Projection - 3D, Sampled, Interpolated in Fourier space ||*]
BP 3D	[Back Projection - 3D, using Euler angles ||]
BP CG	[Back Projection - 3D, Conjugate gradients ||*]
BP R2	[Back Projection - 2D, weighting of image series ||]
BP S2	[Back Projection - 2D, single tilt iterative, constrained ||]
BP W2	[Back Projection - 2D, filtered, weighted ||]

USAGE

.OPERATION: BP RP

<OR>
BP RP,X11

.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 the volume size). 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).]

.SYMMETRIES ANGLES DOC FILE: ANGSYM
[Enter * if the structure has no symmetries.
Otherwise, 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' they transform the volume into itself. The identity operation (angles 0,0,0) MUST be included. The symmetries will be internally enforced on the volume. The reconstruction in this case is calculated as though the projections were multiplied as many times as there are symmetries.]

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

.LAMBDA, CORRECTION LIMIT: 1.0e-4,0.0
[Lambda determines the weight of corrections. Too small a value results in long time of calculations; too large value will terminate the iterations too soon. (Note #3).
Correction limit can be used to terminate the iterations. When the squared correction of the structure becomes smaller than the preset value, the iterations are terminated. When correction limit is set to zero, it will not be used to terminate the program. Iteration limit will be used instead.]

.ITERATION LIMIT, MODE: 25,8
[Program will terminate after number of iterations given.
Mode determines the constraints used:
0 - no constraints,
1 - frequency limit (smoothing),
2 - min constraint,
5 - max constraint.
Any combination of constraints can be used. The mode value should be the sum of any single modes, for example mode=7 activates both min and max constraints, while mode=8 uses all three of them. Constraints are ignored if mode=0, but dummy values should still be entered on the next two lines.]

.MINIMUM, MAXIMUM: 1.77,1.90
[Values of min and max constraints: i.e., the max and min values of the 2D projection data set.]

.SMOOTHING CONST (0-0.999):0.9994
[Smoothing constant determines relative weight of the low-pass filtration. See note #4.]

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. Lambda is used to control the speed of convergence.
   Too small value of lambda will result in a structure that has high frequencies underrepresented. The structure will appear very smooth. Moreover, when such structures are used to estimate the resolution (command RF 3) the Fourier Shell Correlation curve, after initial decrese, will increase in high frequencies region. To remedy the problem, the lambda has to be increased (10 times).
   Too large value of lambda will terminate iterations too soon, earlier than requested number of iterations, usually after first two or three steps. This can be verified in the output stored in the results file. Resulting structure will be incorrect. To remedy this problem the lambda has to be decreased (2 times) and the program has to be repeated. If the problem persists, the lambda has be decreased again until the requested number of iterations is performed.

4. Smoothing constant determines relative weight of the low-pass filtration. It has to be larger than zero and smaller than one. In addition smoothing constant has to be lower than 1/(1+6*lambda). Zero means no smoothing.
   To achieve stronger low-pass filtration effect one can decrease lambda and increase the smoothing constant.
   Approximate frequency response:

    
                lambda     smoothing const    res'n limit (pixels) 
                 .5E-3         0.990                 3 
                 .5E-3         0.997                 5 
                 .1E-3         0.9994               10 
   

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

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

7. An optional register on the OPERATION line receives the number of iterations completed.

8. This operation parallelized for use with MPI.

9. Implemented by: Paul Penczek.

SUBROUTINES

REPS, REDPRQ, RPRQ, ASTA, PREPCUB_S, BCKCQ, PRJCQ, SMT3_Q, DOMIN3_S, DOMAX3_S, DOCORS3_S, BMAX_C, BMIN_C, FMAX_Q, FMIN_Q, HIANG

CALLER

VTIL2