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CV - projection onto ConVex sets -signal restoration

PURPOSE

It performs a 3D restoration by the method of Projections Onto Convex Sets (POCS), which is a restoration technique that is applicable to the problem generated in 3D electron microscopy by the finite tilt angle (missing cone problem) or/and the availability of only single-axis projections (missing wedge problem). This operation includes most of the tools needed to study model data objects that resemble the one you are interested in (a wise precaution before any real data study). COMMAND NOT SUPPORTED

USAGE

.OPERATION: CV

.INPUT1 FILE: DEG001
[Enter the name of the file to be restored.]

.OUTPUT FILE: RES001
[Enter the name of the file where the restored volume is to be kept.]

.MISSING CONE OR WEDGE (OR PREPARE) (C/W/PC/PW): C
[Here you can follow two different directions. If you specify C (Cone) or W (Wedge), it is assumed that you are going to perform the restoration of the signal DEG001 that has been degraded either by the presence of a missing cone (C) or a missing wedge (W). If you specify Prepare Cone (PC) or Prepare Wedge (PW) it is assumed that you are performing a test calculation and that you actually want to degrade the input file by cutting out a cone (PC) or a wedge (PW) in the 3D power spectrum. The degraded file will be the output file. This output can be used as input of future restoration runs.]

.MISSING ANGLE (IN DEGREES): 30
[This is the zenithal angle of either the missing cone or de missing wedge. If PC or PW was specified in the previous question: (i) This will be the last question asked, (ii) The total energy of the input file (that for runs with PC or PW is the original, non-degraded file) will be provided for future use as a constraint in restorations runs.]

FILE FOR THE MODULUS OF THE RESTORED FILE
.OUTPUT: REM001
[This is important in order to appreciate which has been the behaviour of the restoration with respect to the filling of the missing region.]

.SUPLEMENTAL NOISE-FREE MODEL FILE (Y/N): Y
[Answer Y (Yes) if a reference model data is provided. This information will not be used during the restoration itself but it allows the calculation of very important information parameters regarding the quality of the restoration.]

[If answered 'Y' it will then ask:]

SUPLEMENTAL FILE WITH THE TOTAL MODEL
.INPUT: MOD001
[This is the name of the file where the model data are.]

FILE WITH THE MODEL POWER SPECTRUM
.OUTPUT: MOP001
[This file will hold the modulus of the FT of the model. It is assumed that you will be interested in knowing how the model power spectrum is in order to compare it with the results of the restoration.]

.SUPLEMENTAL NOISY MODEL FILE (Y/N): Y
[This is for testing pourposes only. If information about the noisy (but non-degraded) signal is available it should be entered here. It is important since it will allow the calculation of the changes that may be done within the measured region due to the fact that the measurements themselves are noisy.]

[If answered 'Y' it will then ask:]

SUPLEMENTAL FILE WITH THE NOISY MODEL
.INPUT: NOI001
[This is the name of the file where the noisy model is]

[At this step the program will provide with the total energy of the signal to be restored (first question), plus the maximum and manimum density values. This is for information only]

[If noise-free and noisy models were provided the program will calculate at this moment the distance within and outside the missing region between the noise-free and the noisy models. This is important since the distance within the measured area should be used as parameter for the SNR-related constraint.]

.NUMBER OF ITERATIONS: 30
[This is the actual number of times the iterative sequence of constraints will be used.]

.SPHERICAL, CILIN. OR RECTANGULAR LIMITATIONS (S/C/R): S
[It provides two general ways to account for the space limition of the object. One enclosing it into a sphere and the other into s cilinder (both centered at the center of the volume).]

[If answered 'S' it will then ask:]

.SPHERE RADIOUS: 12.0
[This is the radious of the sphere limiting the object extent in real space.]

[If answered 'C' it will then ask:]

.CILINDER RADIOUS: 12.0
[This is the radious of the cilinder.]

.CILINDER HALF-HEIGHT: 7
[The cilinder is assumed to be centered at the origin, the total length of the cilinder is two half-heights.]

[If answered 'R' it will then ask:]

.MAXIMUM AND MINIMUM RECTANGULAR BOND.: 5,27
[They define the allowed rectangular region where the specimen is supposed to exist, in the case of this example it would be between planes 5 and 27 along Z]

.MAXIMUM AND MINIMUM SPECIMEN PIXEL VALUES: 3,1
[It determines the allowed specimen density values. Values higher than the maximum will be set to the maximum, values lower than the minimum will be set to the minimum. This constraint is more general than positivity, although it can be just used as a positivity constraint by setting the maximum value to a very high number and the minimum to 0].

.MAXIMUM AND MINIMUM NON-SPECIMEN PIXEL VALUES: 0.5,0
[This is actually the way that the space-limitation constraint has been implemented. Values outside the specimen-allowed region are projected onto this interval. By setting the two limits to 0 a finite-support constraint is imposed]

.TRANSITION REGION: 2
[It provides a way to generate "soft" specimen boundaries. The meaning of this transition region is the actual number of "layers" around the specimen that will stand between the interior of the region of compact support on which the specimen is defined and what has been defined as "no-specimen". A value of '2', together with a spherical limitation-type spatial constraint ('S') with a value of 12.0 for the radious, and values for the maximum and minimum specimen density values of '3' and '0', means that for radious r=13 the maximum and minimum allowed density values will be 2 and 0, while for radious r=14 they will be 1 and 0. For radious r=15 all density values will be set to 0. This transition region has proven important when dealing with noisy objects.]

.VERY NOISY CASE (Y/N)?: Y
[If the object to be restored is known to be contaminated by noise, then very possible the measured data will not correspond to the expected one for a space-limited signal. If a space limitation constraint is imposed on this data inconsistencies may occur. One good way to deal with these inconsistencies is by allowing the measured data themselves to actually change within some limits (this is the so-called SNR-related constraint). However, it has been empirically proved that in almost all tested cases results are better if the SNR-related constraint is not applied. The exception being very noisy objects. It is a good practice to perform always a restoration with this constraint and compare it with the one performed without this constraint.]

.ENERGY BOND (IN TH.), DISTANCE BOND:
[The energy bod (in units of thousand) is used to apply the energy limitation constraint. The distance bond is only considered if the the SNR-related is going to be applied, it indicates the maximum distance (measured within the measured region) that the restored signal is allowed to differenciate from the original degraded signal.]

NOTES

  1. Not Distributed!

SUBROUTINES

POCS, FFT

CALLER

UTIL1

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