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iradon

逆ra逆变换

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Syntax

I = iradon(R,theta)
I = iradon(R,theta,interp,filter,frequency_scaling,output_size)
[i，h] = iradon（___)

描述

example

I= iradon(R,theta)重建图像Ifrom projection data inRcaptured at projection anglestheta.

I= iradon(R,theta,interp,筛选,frequency_scaling,output_size)specifies parameters to use in the inverse Radon transform. You can specify any combination of the last four arguments.iradonuses default values for arguments that you omit.

[I,H] = iradon（___)also returns the frequency response of the filter,H.

例子

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打开实时脚本

Create an image of the phantom. Display the image.

p =幻影（128）;imshow（p）标题（“原始图像”)

图包含一个轴对象。这axes object with title Original image contains an object of type image.

执行图像的ra转换。

r = ra（p，0：179）;

Perform filtered backprojection.

I1 = iradon(R,0:179);

执行未经过滤的重投影。

I2 = iradon(R,0:179,'linear','none'）；

Display the reconstructed images.

图子图（1,2,1）imshow（i1，[]）标题（“过滤后反射”）子图（1,2,2）imshow（i2，[]）标题（“未经过滤的反击”)

Figure contains 2 axes objects. Axes object 1 with title Filtered Backprojection contains an object of type image. Axes object 2 with title Unfiltered Backprojection contains an object of type image.

打开实时脚本

Create an image of the phantom.

p =幻影（128）;

执行图像的ra换灯，然后以45度角获得投影矢量对应于投影。

r = ra（p，0：179）;r45 = r（：，46）;

执行该单个投影矢量的逆rad radon变换。这iradon语法不允许您直接执行此操作，因为如果theta是a scalar it is treated as an increment. You can accomplish the task by passing in two copies of the projection vector and then dividing the result by 2.

i = iradon（[R45 R45]，[45 45]）/2;

Display the result.

imshow(I, []) title('Backprojection from 45 degrees')

图包含一个轴对象。带有标题反向反射的轴对象45度包含类型图像的对象。

输入参数

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并行光束投影数据，指定为以下之一。

  • 如果theta是a scalar, then specifyRas a numeric column vector containing the Radon transform forthetadegrees.

  • 如果theta是a vector, then specifyRas a 2-D matrix in which each column is the Radon transform for one of the angles intheta.

Data Types:single|双倍的|int8|INT16|INT32|INT64|uint8|UINT16|uint32|uint64|logical

投影角（以度为单位），指定为以下一个。

价值 描述
数字向量 Projection angles. There must be equal spacing between the angles.
数字标量 投影之间的增量角度。预测是从角度进行的m*theta， 在哪里m = 0,1,2,...,size(R,2)-1.
[] 自动将投影之间的增量角度设置为180/size(R,2)

Data Types:双倍的

Type of interpolation to use in the back projection, specified as one of these values, listed in order of increasing accuracy and computational complexity.

价值

描述

“最近”

最近的邻居插值

'linear'

线性插值

“样条”

样条插值
'pchip' Shape-preserving piecewise cubic interpolation
'V5Cubic' Cubic convolution used in MATLAB®5

Data Types:char|string

用于用于频域过滤的过滤器，指定为这些值之一。

价值

描述

“拉姆拉克”

Cropped Ram-Lak or ramp filter. The frequency response of this filter is |f|。由于此过滤器对投影中的噪声很敏感，因此以下列出的过滤器之一可能是可取的。这些过滤器将Ram-Lak滤波器乘以去强调高频的窗口。

'Shepp-Logan'

将拉姆拉克过滤器乘以sinc功能

“余弦”

将拉姆拉克过滤器乘以余弦功能

'Hamming'

将拉姆拉克过滤器乘以Hamming window

'Hann'

将拉姆拉克过滤器乘以Hann window
'没有任何' 没有过滤。iradon返回过滤backprojection data.

Data Types:char|string

Scale factor for rescaling the frequency axis, specified as a positive number in the range (0, 1]. Iffrequency_scaling是less than 1, then the filter is compressed to fit into the frequency range[0,frequency_scaling]，以归一化频率；上面的所有频率frequency_scalingare set to0.

重建图像中的行和列数，指定为正整数。如果output_size是not specified, the size is determined from the length of the projections according to:

output_size = 2*地板（尺寸（大小）（R,1)/(2*sqrt(2)))

如果指定output_size, theniradonreconstructs a smaller or larger portion of the image but does not change the scaling of the data. If the projections were calculated with theradon函数，然后重建的图像可能与原始图像不一样。

Output Arguments

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Grayscale image, returned as a numeric matrix. If input projection dataR是data typesingle, thenI是single;否则I是双倍的.

Data Types:single|双倍的

过滤器的频率响应，返回为数字向量。

Data Types:双倍的

算法

iradon假设旋转中心是投影的中心点，定义为ceil(size(R,1)/2).

iradonuses the filtered back projection algorithm to perform the inverse Radon transform. The filter is designed directly in the frequency domain and then multiplied by the FFT of the projections. The projections are zero-padded to a power of 2 before filtering to prevent spatial domain aliasing and to speed up the FFT.

参考

[1] Kak, A. C., and M. Slaney,Principles of Computerized Tomographic Imaging, New York, NY, IEEE Press, 1988.

Extended Capabilities

Version History

在R2006a之前引入

See Also

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