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BP MEM2 - Back Projection - 2D maximum entropy method

(8/12/96)

PURPOSE

Calculates 2-dimensional reconstruction using Maximum Entropy Method. The projections need not have power-of-two dimensions.

SEE ALSO

BP 3 [Back Projection - 3D, iterative]
BP 3D [Back Projection - 3D, using Euler angles, ||]
BP 3E [Back Projection - 3D, using Euler angles]
BP CTF [Back Projection - 3D, CTF correction, ||]
BP GW [Back Projection - weighted, arbitrary geometry]
BP GW3 [Back Projection - weighted, arbitrary geometry, 3 angles]
BP R2 [Back Projection - 2D, R**2 weighting of the image series]
BP RP [Back Projection - 3D, iterative, with constraints, ||]
BP S2 [Back Projection - 2D, single tilt iterative, with constraints]
BP W2 [Back Projection - 2D, filtered weighted]
BP WX [Back Projection - weighted, X]
BP WY [Back Projection - weighted, Y]
BP XY [Back Projection - simple for single axis & conical tilting]

USAGE

.OPERATION: BP MEM2

.PROJECTIONS: PRO***
[Enter the prefix of the projection file series.]

.FILE NUMBERS: 1-20,33,45-128
[Enter number of files containing projections.]

.SLICE NUMBER, RADIUS OF RECONSTRUCTED CIRCLE: 23,52
[Enter number of slice to be reconstructed and the radius of the reconstructed circle.]

.SEARCH DIRECTIONS, ENTROPY TYPE: 3,1
[Number of gradient search directions for the optimization program: only 3, 4 or 6 is allowed. Three directions are sufficient.

Entropy type determines the definition of the entropy to be used:

0 - fixed default value - the average of the reconstructed image is kept constant and equal to the default value;

1 - variable average, no default value needed;

2 - not supported;

3 - not supported;

4 - values of reconstructed object are kept 0<f<1 at fixed default value. This option can be treated as the constraint of maximum value of the reconstruction provided that the projections are scaled properly.]

.C_AIM, VARIANCE: 1000,1
[C_aim is the expected chi-squared error used for convergence test. Variance is the error of each pixel. Only a constant error model is used. Note that the two numbers are related.]

.STARTING VALUE, DEFAULT VALUE: 0.1,0.2
[Starting value used as a background for the reconstructed image. It must be positive. A good guess is 1/N, where N is the number of reconstructed pixels. Default value is used for maximization of entropy type 0 or 4.]

.ITERATION LIMIT, CONVERGENCE TEST: 100,1
[Iteration limit prevents excessively long calculations.

Convergence test defines the stopping criterion used:

1 - C <= 1.005*C_aim or TEST <= 0.01;

2 - as in opt. 1, but stop after 8 iterations if TEST starts increasing;

3 - as in opt. 1, but stop if C changes by less than 1%.]

.PRINT INFORMATION EACH ITERATION STEP (Y/N): N
[Self-explanatory.]

.SCALING FACTOR: 1.0
[Projections are multiplied be this factor. It simplifies adjustment of the projections' values to obey constraints.]

.RECONSTRUCTED 2-D FILE: SLI023
[Name of output file.]

NOTES

  1. The projection angle must be provided in the position THETA of the header of each file.

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

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

  4. Implemented by: P. Penczek.

CALLER

VTIL2

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