fan2para
Convert fan-beam projections to parallel-beam
Description
uses name-value arguments to control aspects of the data conversion.P
= fan2para(F
,D
,Name,Value
)
[
returns the parallel-beam sensor locations in P
,paraSensorPos
,paraRotAngles
] = fan2para(___)paraSensorPos
and
rotation angles in paraRotAngles
.
Examples
Recover Parallel-beam Data from Fan-beam Data
Create synthetic parallel-beam data.
ph = phantom(128);
Calculate the parallel beam transform and display it.
theta = 0:179; [Psynthetic,xp] = radon(ph,theta); imshow(Psynthetic,[],... 'XData',theta,'YData',xp,'InitialMagnification','fit') axis normal title('Synthetic Parallel-Beam Data') xlabel('\theta (degrees)') ylabel('x''') colormap(gca,hot), colorbar
Convert the parallel-beam data to fan-beam.
Fsynthetic = para2fan(Psynthetic,100,'FanSensorSpacing',1);
Recover original parallel-beam data.
[Precovered,Ploc,Pangles] = fan2para(Fsynthetic,100,... 'FanSensorSpacing',1,... 'ParallelSensorSpacing',1); figure imshow(Precovered,[],... 'XData',Pangles,'YData',Ploc,'InitialMagnification','fit') axis normal title('Recovered Parallel-Beam Data') xlabel('Rotation Angles (degrees)') ylabel('Parallel Sensor Locations (pixels)') colormap(gca,hot), colorbar
Input Arguments
F
— Fan-beam projection data
numeric matrix
Fan-beam projection data, specified as a numeric matrix. Each column of
F
contains the fan-beam data at one rotation angle. The number of
columns indicates the number of fan-beam rotation angles and the number of rows
indicates the number of fan-beam 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. fan2para
assumes that the center of rotation is
the center point of the projections, which is defined as
ceil(size(F,1)/2)
. The figure illustrates D
in
relation to the fan-beam vertex for one fan-beam projection.
Data Types: double
| single
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: P = fan2para(F,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: P = fan2para(F,D,"FanRotationIncrement",5)
specifies a fan
rotation increment of 5 degrees.
FanCoverage
— Range of fan-beam rotation
"cycle"
(default) | "minimal"
Range of fan-beam 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
— Fan-beam rotation angle increment
1
(default) | positive scalar
Fan-beam rotation angle increment in degrees, specified as a positive scalar.
Data Types: double
FanSensorGeometry
— Fan-beam sensor positioning
"arc"
(default) | "line"
Fan-beam 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 fan-beam vertex.
|
|
| Sensors are spaced at equal distances along a line that is
parallel to the x' axis. The closest sensor
is distance
|
|
FanSensorSpacing
— Fan-bean sensor spacing
1
(default) | positive scalar
Fan-bean 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 fan-beams, in pixels. Linear spacing is measured on the x' axis.
Data Types: double
Interpolation
— Type of interpolation
"Linear"
(default) | "nearest"
| "spline"
| "pchip"
Type of interpolation used between the parallel-beam and fan-beam data, specified as one of these values.
"nearest"
— Nearest-neighbor
"linear"
— Linear (the default)
"spline"
— Piecewise cubic spline
"pchip"
— Piecewise cubic Hermite (PCHIP)
ParallelCoverage
— Range of parallel-beam rotation
"halfcycle"
(default) | "cycle"
Range of parallel-beam rotation, specified as "halfcycle"
or
"cycle"
.
"cycle"
— Parallel data covers the full range of [0, 360) degrees."halfcycle"
— Parallel data covers [0, 180) degrees.
ParallelRotationIncrement
— Parallel-beam rotation angle increment
positive scalar
Parallel-beam rotation angle increment in degrees, specified as a positive scalar
k such that 180/
k is an
integer. If you do not specify ParallelRotationIncrement
, then
the default value is equal to FanRotationIncrement
.
Data Types: double
ParallelSensorSpacing
— Parallel-beam sensor spacing
positive scalar
Parallel-beam sensor spacing in pixels, specified as a positive scalar. The range
of parallel-beam sensor locations is computed from the range of fan angles,
fanAngles, according to: [
.D
*sin(min(fanAngles))
D*sin(max(fanAngles))]
If you do not specify ParallelSensorSpacing
, then the spacing
is assumed to be uniform and is set to the minimum spacing implied by the fan angles
and sampled over the range implied by the fan angles.
Data Types: double
Output Arguments
P
— Parallel-beam projection data
numeric matrix
Parallel-beam projection data, returned as a numeric matrix. Each column of
P
contains the parallel-beam data at one rotation angle. The number
of columns indicates the total number of parallel-beam rotation angles and is equal to
the length of paraRotAngles
. The number of rows indicates the total
number of parallel-beam sensors and is equal to the length of
paraSensorPos
.
Data Types: double
paraSensorPos
— Parallel-beam sensor locations
numeric column vector
Parallel-beam sensor locations, returned as a numeric column vector.
Data Types: double
paraRotAngles
— Parallel-beam rotation angles
numeric row vector
Parallel-beam rotation angles, returned as a numeric row vector.
Data Types: double
Version History
Introduced before R2006a
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