para2fan
Convert parallelbeam projections to fanbeam
Description
converts the parallelbeam data F
= para2fan(P
,D
)P
to the fanbeam data
F
. Each column of P
contains the parallelbeam
sensor samples at one rotation angle. D
is the distance from the
fanbeam vertex to the center of rotation.
The parallelbeam sensors are assumed to have a onepixel spacing. The parallelbeam rotation angles are spaced equally to cover [0, 180] degrees. The calculated fanbeam rotation angles have the same spacing as the parallelbeam rotation angles, and cover [0,360) degrees. The calculated fanbeam angles are equally spaced with the spacing set to the smallest angle implied by the sensor spacing.
uses namevalue arguments to control aspects of the data conversion.F
= para2fan(P
,D
,Name,Value
)
[
returns the fanbeam sensor locations in F
,fanSensorPos
,fanRotAngles
]
= para2fan(___)fanSensorPos
and rotation
angles in fanRotAngles
.
Examples
Convert Parallelbeam Projections to Fanbeam Projections
Generate parallelbeam projections
ph = phantom(128); theta = 0:180; [P,xp] = radon(ph,theta); imshow(P,[],'XData',theta,'YData',xp,'InitialMagnification','fit') axis normal title('ParallelBeam Projections') xlabel('\theta (degrees)') ylabel('x''') colormap(gca,hot), colorbar
Convert to fanbeam projections
[F,Fpos,Fangles] = para2fan(P,100); figure imshow(F,[],'XData',Fangles,'YData',Fpos,'InitialMagnification','fit') axis normal title('FanBeam Projections') xlabel('\theta (degrees)') ylabel('Sensor Locations (degrees)') colormap(gca,hot), colorbar
Input Arguments
P
— Parallelbeam projection data
numeric matrix
Parallelbeam projection data, specified as a numeric matrix. Each column of
P
contains the parallelbeam data at one rotation angle. The
number of columns indicates the number of parallelbeam rotation angles and the number
of rows indicates the number of parallelbeam sensors.
Data Types: double
 single
D
— Distance from fan beam vertex to center of rotation
positive number
Distance in pixels from the fan beam vertex to the center of rotation, specified as
a positive number. para2fan
assumes that the center of rotation is
the center point of the projections, which is defined as
ceil(size(F,1)/2)
. The value of D
must be
greater than or equal to
. The figure illustrates ParallelSensorSpacing
*(size(P,1)1)/2D
in relation to the
fanbeam vertex for one fanbeam projection.
Data Types: double
 single
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: F = para2fan(P,D,FanRotationIncrement=5)
specifies a fan
rotation increment of 5 degrees.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: F = para2fan(P,D,"FanRotationIncrement",5)
specifies a fan
rotation increment of 5 degrees.
FanCoverage
— Range of fanbeam rotation
"cycle"
(default)  "minimal"
Range of fanbeam rotation, specified as "cycle"
or
"minimal"
.
"cycle"
— Rotate through the full range [0, 360) degrees."minimal"
— Rotate through the minimum range necessary to represent the object.
FanRotationIncrement
— Fanbeam rotation angle increment
positive scalar
Fanbeam rotation angle increment in degrees, specified as a positive scalar.
If
FanCoverage
is"cycle"
, then360/FanRotationIncrement
must be an integer.If you do not specify
FanRotationIncrement
, then the default value is equal to the parallelbeam rotation angle.
Data Types: double
FanSensorGeometry
— Fanbeam sensor positioning
"arc"
(default)  "line"
Fanbeam sensor positioning, specified as "arc"
or
"line"
.
Value  Meaning  Diagram 

 Sensors are spaced at equal angles along a circular arc. The center of the arc is the fanbeam vertex.


 Sensors are spaced at equal distances along a line that is
parallel to the x' axis. The closest sensor
is distance


FanSensorSpacing
— Fanbeam sensor spacing
positive scalar
Fanbeam sensor spacing, specified as a positive scalar.
If
FanSensorGeometry
is"arc"
, thenFanSensorSpacing
defines the angular spacing in degrees.If
FanSensorGeometry
is"line"
, thenFanSensorSpacing
defines the linear distance between fanbeams, in pixels. Linear spacing is measured on the x' axis.
If you do not specify FanSensorGeometry
, then the default
value of FanSensorSpacing
is the smallest value implied by
ParallelSensorSpacing
such that:
If
FanSensorGeometry
is"arc"
, thenFanSensorSpacing
is180/pi*asin(
ParallelSensorSpacing
/D
)If
FanSensorGeometry
is"line"
, thenFanSensorSpacing
isD
*asin(ParallelSensorSpacing
/D
)
Data Types: double
Interpolation
— Type of interpolation
"Linear"
(default)  "nearest"
 "spline"
 "pchip"
Type of interpolation used between the parallelbeam and fanbeam data, specified as one of these values.
"nearest"
— Nearestneighbor
"linear"
— Linear (the default)
"spline"
— Piecewise cubic spline
"pchip"
— Piecewise cubic Hermite (PCHIP)
ParallelCoverage
— Range of parallelbeam rotation
"halfcycle"
(default)  "cycle"
Range of parallelbeam rotation, specified as "halfcycle"
or
"cycle"
.
"cycle"
— Parallel data covers the full range of [0, 360) degrees."halfcycle"
— Parallel data covers [0, 180) degrees.
ParallelSensorSpacing
— Parallelbeam sensor spacing
1
 positive scalar
Parallelbeam sensor spacing in pixels, specified as a positive scalar.
Data Types: double
Output Arguments
F
— Fanbeam projection data
numeric matrix
Fanbeam projection data, returned as a numeric matrix. Each column of
F
contains the fanbeam sensor samples at one rotation
angle.
Parallelbeam projection data, returned as a numeric matrix. Each column of
F
contains the fanbeam data at one rotation angle. The number of
columns indicates the total number of fanbeam rotation angles and is equal to the
length of fanRotAngles
. The number of rows indicates the total
number of parallelbeam sensors and is equal to the length of
fanSensorPos
.
Data Types: double
fanSensorPos
— Fanbeam sensor locations
numeric column vector
Fanbeam sensor locations, returned as a numeric column vector.
If
FanSensorGeometry
is"arc"
(the default), thenfanSensorPos
contains the fanbeam sensor measurement angles.If
FanSensorGeometry
is"line"
, thenfanSensorPos
contains the fanbeam sensor positions along the line of sensors.
Data Types: double
fanRotAngles
— Fanbeam rotation angles
numeric row vector
Fanbeam rotation angles, returned as a numeric row vector.
Data Types: double
Version History
Introduced before R2006a
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