Salvatore Lanzavecchia, Francesca Cantele and Pier Luigi Bellon
(Dip. Chimica Strutturale e Stereochimica Inorganica, Via Venezian 21, 20133 Milano, Italy)
(email: francesca.cantele@unimi.it)
Bernard Heymann
(Rm 1515, 50 South Dr., NIH, Bethesda, MD, 20892, USA)
20050707
The Radon package provides the following two programs:
1)
radon: Forward and backward Radon
transformation, and POCS filtering of a Radon transform.
2)
radonrecon: Reconstruction of a Radon
transform from 2D projection images.
The Radon package uses several functions from the Bsoft package.
Bsoft must be installed in a location indicated by the BSOFT
environmental variable, typically:
setenv BSOFT
/usr/local/bsoft
The latest version of Bsoft can be obtained
from http://www.br.caltech.edu/~bheymann/bsoft/bsoft.html.
Tar file:
Gzipped tar file:
The tar distribution unpacks into a directory called "radon".
Typically, the package should be installed in the directory
/usr/local/radon:
cd /usr/local
tar xzvf radon.tgz
Compile the package:
cd /usr/local/radon
makerad
Make sure
the following variables are set appropriately in your shell:
setenv RADON /usr/local/radon
setenv BSOFT
/usr/local/bsoft
setenv PATH
${RADON}/bin:${BSOFT}/bin:$PATH
setenv
LD_LIBRARY_PATH ${BSOFT}/lib
Typing the program name only produces a list of options. There are
defaults for most of the options.
All images must be square
for 2D and cubic for 3D, with the edges powers of 2. If the image
size is not a power of 2, it will be resized to the next power of 2.
A Radon transform is an array of size radii * angles * angles, where
the radial size (NCOL) is the same as the edge of the image, and the
number of angles (NTHETA) covers the range 0  2*PI. Because half of
this angular range is redundant, a smaller transform is calculated
with the number of angles covering 0  PI equal to the image edge
size (NTHETA/2 = NCOL).The POCS filter imposes consistency on a Radon
transform and can be used to fill in missing points.
1)
radon [options] input.img output.img
There are three
actions defined to do the forward and backward transformations, and
the POCS filtering. One or more of these actions must be used to get
output.
a) To compute a Radon transform:
radon v 7 forward 4 kernel 11,2 ico.map ico.rad.map
b)
To compute a backward Radon transform:
radon v
7 backward 4 kernel 15,4 ico.rad.map ico.img.map
c)
To filter a Radon transform:
radon v 7 pocs
5,7 mask ico.mask.map ico.rad.map ico.radf.map
d)
To do all three operations with one command line:
radon v 7 for 4 pocs 10,1 back 4 ker 11,2 ico.map
ico.img.map
2) radonrecon [options]
input.star [input.star]
All the required parameters are
obtained from the STAR file, including the projection image files
(with paths). The origins and orientations of the projection images
must be specified correctly in the STAR file, following the
conventions in Bsoft. The STAR file also incorporates a mechanism to
indicate selected projection images, which can be manipulated using
several Bsoft programs. Symmetryrelated views are calculated for
each projection image when it is incorporated into the
reconstruction.
radonrecon v 7 origin 32,32,32
mask ico.mask.map out out.star rec ico.rec.map sym I90
ico.star
A mask image is calculated for the angular coverage
of orientation space and used to weigh the reconstruction. This image
can be used with the POCS filter to fill in missing points in the
reconstruction.
The real space map is then calculated (shown below):
radon v 7 backward 4 kernel 15,4 ico.rec.map
ico.real.map
The conventions in the Radon package
follow those of the Bsoft package.
Euler angles are defined
with respect to the view vector {x,y,z} and the rotation angle {a}
around this vector:
phi = atan(y, x);
theta = acos(z);
psi = a  phi;
The
origin for 2D and 3D images is defined as its offset (in pixels) from
the first pixel (voxel) in the image array and typically coincides
with symmetry origin for symmetric objects. Shifts are calculated as
the difference between the projection image origin and the
reconstruction origin.
Symmetry notation:
Symmetry 
Notation 
Examples 
Cyclic 
C<n> 
C2, C3, C4 ... 
Dihedral 
D<n> 
D2, D3, D4 ... 
Tetrahedral 
T 
T 
Octahedral 
O 
O 
Icosahedral 
I 
I 
(alternative) 
I90 

The alternative I90 notation for icosahedral objects indicates a 90 degree rotation of the standard icosahedral view and is adopted by some electron microscopy packages.
Lanzavecchia S., Bellon P.L. and Radermacher M. "Fast and accurate three dimensional reconstruction from projections with random orientations via Radon transforms." J. Struct. Biol. 128, 152164, 1999.
Lanzavecchia S., Cantele F., Radermacher M. and Bellon P.L. "Symmetry embedding in the reconstruction of macromolecular assemblies via the discrete Radon transform." J. Struct. Biol., 137, 259272, 2002.