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Data acquisition and processing

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Data acquisition modes

As it was mentioned earlier during the data acquisition the x-ray source and the detector are rotating around the axis of rotation of the gantry and acquiring projection data from the object located between them. The rotational motion can be continuous or stepping. In continuous mode the projection data is blurred and it is relative to the arc rotated during the readout time of the detector. In case of fast readout detectors this is negligible, and this effect can be controlled by the adjustment of the rotation speed to the readout time. If the rotational motion is done in steps (step and shoot mode) the blurring can be avoided, but the start and stop cycles of the motion increase the acquisition time. Nevertheless this latter method is useful to image ex-vivo samples with high resolution, while the continuous motion is beneficial to image living and moving objects.

Circular scan

If the holder of the object stands still during the rotation, then the x-rays draw a circular orbit on the surface of the object. This acquisition mode called circular scan. In this case the x-rays in the middle of the field of view are parallel to the reconstruction plane, therefore the image quality of the corresponding slices are excellent. However the slices located at the edge of the field of view has an increasing angle to the x-rays, therefore their image quality is deteriorated and characteristic artefacts appear (cone-beam artefact). In circular mode the acquisition time is equal to the duration of one rotation and the axial scan range is to one axial field of view.


Spiral scan

In order to image an object extending over the axial field of view of the detector multiple circular scan can be performed one after the other. This can be time consuming and the image quality will vary along the z-axis due to the cone-beam artefact mentioned earlier. Another option is to continuously move the table during the rotation. The x-rays draw a spiral on the surface of the object, therefore this acquisition mode is called to helical or spiral scan.
Similarly to the third generational human CT systems the ratio of the table translation over one rotation to the axial field of view is called to pitch. It is equal to one, when the table moves exactly one axial field of view per rotation. If the pitch was bigger than one there are gaps in the axial coverage and interpolation should be used to calculate the missing raw data. In contrary if the pitch was bigger than one the spiral orbits will overlap, so the same region is scanned over more than one rotation. The higher the pitch the lower the acquisition time, however the image quality is also lower (see Table 3).

The biggest advantage of the spiral scan is that reconstructed slices have homogeneous image quality and the acquisition time is shorter in compare to multiple circular scanning. Although the scan range has to be extended in order to reconstruct the entire selected volume, this usually does not cause problems in practice.

Circular Multi circulars Helical/Spiral
Number of rotations (N) 1 N SR/p
Rotation time (trot) trot trot trot
Table travel speed 0 0 (AFOV•p)/ trot
Scan range (SR) AFOV N•AFOV SR
Scan time trot N•trot trot•SR/p

Table 3 Comparison of the parameters of different scan modes AFOV – axial field of view, p – pitch.

Other orbits

Reconstructions based on filtered backprojection (FBP) algorithm gives the best result if the data was collected with homogeneous sampling. This requires collecting the projection data with equal sampling both along the table translation and over the gantry rotation. Conversely, iterative algorithms can reconstruct images from incomplete projection data or form smaller number of projections making possible to reconstruct the volume even in special cases, when it was not possible to perform a complete, uniform scanning of the object. Iterative algorithms are used for example for scanning large sized printed circuit boards (see NDT, non-destructive testing), where depth information is ensured by scanning along a surface with largest available solid angle.

Acquisition parameters

The parameters are usually selectable on a cone-beam CT system console together with their description and their typical values are shown in the Table 4.

Parameter Description Typical range
Tube voltage The accelerator voltage of the x-ray tube. Determines the maximum energy of the x-ray beam. Discrete values 30 - 80 kVp
Tube current The heating current of the x-ray cathode. Defines the amount of the accelerated electrons, thus the intensity of the generated x-ray beam. Continuous values 0.1 – 10 mA
Exposure time Integration time of the x-ray detector 10 – 5 000 ms
Number of projections Number of projections collected per rotation. It is also referred as angular sampling. 180 – 720
Binning Possibility to sum the data of the neighbouring pixels of the detector. It lowers the noise of the raw data but also decrease the achievable spatial resolution. 1x1 – 4x4
Pitch The ratio of the table translation over one rotation to the axial field of view. It defines the sampling in the z-direction. 0.5 – 1.5
Zoom factor Defined as a ratio of the field of view to the active surface of the detector. ~1.2x – 1000x

Table 4. Parameters are usually selectable on a cone-beam CT system console

Raw data processing

The Figure 3 shows a practical example of the raw data processing performed after the data acquisition. The data is acquired by a frame grabber card connected directly to the X-ray detector and transferred to the memory of the acquisition PC. In order to speed up the read out of the detector several pixels are read out in parallel and their signal is serialized. Therefore the first step is to sort them into the right order to form the columns and rows. This step is called to deinterlace. If the full resolution is not required then the projections can be resized.
The data is transferred form the system memory to the memory of the GPU (graphical processing unit), which can perform the reconstruction in real time together with all the projection level corrections. Following the offset, gain and bad pixel corrections the projections are saved for further processing and also transferred to the reconstruction where following a geometrical correction step they are backprojected. After all the data is processed the reconstructed volume is displayed and saved.

Figure 3 Raw data processing and reconstruction steps in a cone-beam CT system (example)



Offset correction

The dark current (also known as offsets) is a leaking current on the photodiodes, which cause a measurable signal for a detector without X-ray illumination. The magnitude of the signal increases linearly with exposure time, and in case of texp=0, its value is greater than zero. Each offset value of the detector pixel changes due to temperature, increasing the temperature with 10 Celsius degrees causes doubled value. Thus, if the detector environment temperature changed, it is necessary to recalibrate the offset. The dark current value varying from pixel to pixel, its detector surface distribution is not uniform (see Figure 4).

During the calibration of the dark current, each pixel is measured on the further applied exposure time, and the resulting matrices are stored and subtracted from collected raw images. If the offset matrices are miscalibrated, slightly dark circles appear on the homogeneous areas of the reconstructed image.

Figure 4 Offset image of a 7-panel detector (RadEye7H). It can be seen that each panel has different dark current average from one another; the highest (light) is from the left of the first and 4 panel, while the lowest (dark) is in the sixth panel.


Gain correction

For good image quality, it is needed that for homogeneous radiation in the detector should result homogeneous images. The individual diodes have different response for the input signal for each pixel, because of the nonlinear sensitivity.

Figure 5 Image of a 7-panel detector (RadEye7H) without gain correction. One can see that in spite of the homogeneous illumination the detector image is not homogeneous because of the different sensitivity of individual pixels.

The target of gain calibration is to change each pixel's locally varying characteristics to a common linear response function of the detector. During the calibration the response functions for each pixel is determined according to a predefined tube current and tube voltage. In general, the input signal is the multiplication of the tube current and exposure time, but in this case the time-dependency is examined in addition to constant current. The characteristic of the signal-response function can be described accurately with polynomial; its order depends on the specific system (e.g. the type of detector). After the correction, the attenuated X-rays should result same intensity in each pixel, if a homogeneous and constant thickness of absorbing object is placed between the x-ray source and detector.

Figure 6 The X-ray detector response function in term of the illumination.

If the gain correction values are obsolete, then ring artefacts appear on the homogeneous areas of reconstructed images, like the failure of dark current correction.

Beam-hardening correction

For monochromatic beam the attenuation in a homogenous object is described by the Lambert-Beer law. In voxelized environment this can be written as follows:

y_i=I_0 \cdot e^{- \sum_{j=1}^{N}(l_{ij}\mu_j)}


  • yi is the intensity measured in the i-th pixel
  • I0 intensity comes from source
  • µj the mass attenuation coefficient in the j-th voxel
  • lij the length of the beam passing through the j-th voxel comes from the source to the i-th pixel

The Feldkamp-type reconstruction is based on monochromatic beam. In practice, the spectrum of X-ray is an extended continuous function. Because the absorption of materials are energy dependent, furthermore the different materials reduce the intensity in varying degrees, characteristic artefacts arise on the uncorrected reconstructed image that a real uniform attenuation area (e.g. water-filled cylinder) has a descending intensity profile towards the centre (see Figure 7). Since for the lower energies have greater attenuation, in a certain thickness of medium the low-frequency components can disappear from the spectrum. The name refers to this phenomenon, the spectrum of high-energy "hard" part retained after the transmission. Accordingly, on the reconstructed images of a homogeneous phantom the absorption is not uniform but decreases toward the centre of the phantom. This phenomenon is well explained by the fact that at the edge of the phantom during penetration, even a low-energy components are also present, where the absorption is higher, but they are completely absorbed in the middle.

Figure 7 Beam-hardening effect and correction. The upper left picture shows a water-filled cylinder beam-hardening corrected homogeneous cross-sectional image, below the yellow line corresponding profile curve. The upper right is the image of the same cylinder without beam-hardening correction and the corresponding profile curve is shown below.

Correction can be made by hardware or software filtering. In case of hardware filtering (see Mechanical filters in Section) metal filter (e.g. aluminium) mounted in front of the X-ray tube absorb the low-energy parts of the spectrum directly after the exit from the tube. Unfortunately, the filters are only partially selective and beside the low-energy components, the high-energy range of the spectrum are reduced, thereby reduce the light intensity and increase the image noise. Therefore, in practice, in additional to the hardware filter, software algorithms are applied on the projections or reconstructed images.

Bad pixel correction

A pixel is assigned as defective if, after the above corrections (offset, gain, and projection level beam-hardening) the input signal of this pixel is significantly different from its environment. If a pixel’s dark current is too large, the response during exposure can be saturated and therefore false information can be gained out of it. The aim of the calibration is to find these pixels and to correlate with the saturation value. Another problem if the intensity of a pixel in the offset-corrected image is very different from the average, the gain correction cannot be used because the pixel value is too low (does not respond to illumination) or saturates over a particular exposure time. The defective pixels found in the calibration can be stored in a mask, and using the neighbouring pixels based interpolation can be corrected.
The defective pixels cause usually a sharply contrasting environment, circular artefacts in the reconstructed image.

Geometric calibration

Although during the CT acquisition, the X-ray detector and tube mounted on a common mechanical frame and performs rotation through pre-known positions; but for reconstruction of the images with high spatial resolution (~ 10μm) the relation of the tube and the detector to the axis of rotation should be determined greater precision than the mechanical accuracy. In the back-projection step of the reconstruction there is a need for accurate knowledge of geometrical parameters of the system, otherwise the quality of the reconstructed image is greatly reduced.
The determination of the geometric parameters of the cone-beam CT coordinate system described on Coordinate system of the cone-beam CT) can be done in many ways. In the course of the most commonly used calibration procedure a phantom with high attenuation point objects (e.g. ball bearings) with known distance from each other is measured. When the centre of objects found in each projection of the total turn around, a continuous, angular position dependent model can be fit each centre of masses. The system geometry can be calculated from the fitting parameters. The parameters can be constants or gantry angle dependent. A proper model function, which is based on the following equations:

Y(\theta)=D \frac{-x_{\nu}sin(\theta)+y_{\nu}cos(\theta)}{D-d+x_{\nu}cos(\theta)+y_{\nu}sin(\theta)}+E_y (\theta)


Z(\theta)=D \frac{-z_{\nu}}{D-d+x_{\nu}cos(\theta)+y_{\nu}sin(\theta)}+E_z (\theta)


  • D distance between focal point and the detector
  • d distance between focal point and axis of radius of rotation
  • Ey and Ez is the distance between the focal point and the normal of the detector placed to the centre of the detector
  • x_{\nu}, \; y_{\nu}, \; z_{\nu} position of the point sources
  • Y, Z the mapped coordinates of the point sources in the coordinate system of the detector
  • \theta gantry position


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