Introduction

The primary purpose of Cone-beam CT (CBCT) is to improve patient set-up during treatment using its three dimensional (3D) imaging capabilities. As the CBCT covers a wider field of view (FOV), a greater contribution of X-ray scatter presents a challenge in obtaining acceptable image quality. In the pursuit of using CBCT datasets for treatment planning and adaptive radiotherapy (ART) [1], optimal image quality is essential to localise the position of the tumour in 3D and to register any changes in tumour and patient anatomy during the treatment. For disease sites like lung, liver and prostate, where intrafractional motion is significant, fusion of CBCT images with planning CT images based on soft tissue anatomy can be performed using deformable image registration algorithms [2, 3]. However, the accuracy of deformable registration algorithm to recover the deformations depends on image quality.

A quality assurance (QA) program for image quality of CBCT guidance has been established in order to address the unique performance of each CBCT system [4]. This QA tool helps to demonstrate the high linearity of CT numbers, uniformity and spatial resolution of several CBCT systems and provides a tolerance limit for each parameter. Several studies [5, 6] have evaluated the image quality characteristics such as noise and spatial resolution of CBCT based on QA program. In these studies, the image quality parameters have been compared for different tube current settings [6] and different reconstruction methods [5]. Many studies [7–10] have evaluated the CBCT image quality influenced by noise and resolution for its use in the guidance of radiation therapy on a medical linear accelerator. However, the relationship between image noise and resolution in a clinical CBCT system due to the effect of reconstruction filters has not been evaluated so far. In CBCT, apart from scanner geometry and characteristics, the reconstruction filters also influence the image quality with greater effects on noise and resolution [11]. Hence it is essential to assess the effect of different reconstruction filters on noise and spatial resolution. This study uses the Varian On-Board Imager (OBI) cone-beam CT images of the Catphan 504 and image quality parameters of contrast-to-noise ratio (CNR), uniformity, pixel stability and spatial resolution were assessed for full-fan and half-fan acquisition modes using different reconstruction filters. The resultant images were evaluated quantitatively to examine the effects of reconstruction filters on image quality.

Materials and methods

In this study a Varian OBI integrated with an iX Clinac at 90° with respect to the treatment beam is used (Varian Medical Systems, Palo Alto, CA, USA). It provides three modes of imaging: kV radiography, CBCT and fluoroscopy. The OBI consists of a kV X-ray source (0.4 and 0.8 mm focal spots) and a kV amorphous silicon flat panel imaging detector opposing each other. For reconstruction diameters up to 24 cm, a full-fan mode is used where the beam central axis passes through the detector centre in order to acquire full-fan projections of the entire object in a single rotation. A total of 360 projections during the 200° gantry rotation are obtained in full-fan acquisition. Imaging in full-fan mode used 100 kVp, 20 mA and 20 ms. For a larger reconstruction diameter of up to 45 cm, the CBCT acquisition is switched to half-fan mode, in which the detector is offset by 14.8 cm to acquire 655 projections during 360° gantry rotation. During this mode, one half of the projections are obtained from one-half-fan and the other half is obtained from half-fan projections from other directions. Imaging in half-fan mode used 125 kVp, 80 mA and 13 ms. A full- or half-bow-tie filter is added to the kV source while scanning depending on the acquisition mode. The CBCT version used is v2.1 and OBI v1.5.

The Catphan 504 phantom (The Phantom Laboratory, New York, USA) is a cylindrical phantom build of several modules that can be used to measure various image quality indices. The phantom has a diameter of 20 cm and length of 20 cm. The modules used for this study were the following: CTP404 containing inserts of different densities are used for HU linearity—this includes air, polystyrene, low-density polyethylene, acrylic, Delrin and Teflon with densities in the range 0–2.16 g/cm3; CTP 486 has uniform water equivalent disk of 150 mm diameter to evaluate HU uniformity; CTP 528 is used to evaluate spatial resolution with up to 21 line pairs/cm.

The 2D projection data of the Catphan 504 phantom were acquired for both full-fan and half-fan modes of CBCT. Using the Radon transform in Matlab (The MathWorks Inc., Natick, MA, USA), the sinograms of the image intensity along the radial line for the specified angle were generated. These sinograms were then utilised for reconstructing the images in Matlab using different filters. The various steps involved in reconstruction process is described below as flowchart.

figure a

Five different filters (Ram-Lak, Shepp-Logan, Cosine, Hamming and Hann) were applied during back projection to manipulate the reconstructed images. Each filter was defined by modifying the ideal Ramp filter (which is the Ram-Lak filter) in the frequency domain according to the window needed to deemphasize high frequencies [12] as in Eq. 1 below.

$${\text{H}}\left( {{\omega }} \right) = \left| {{\omega }} \right|{\text{W}}\left( {{\omega }} \right)$$
(1)

where ω is the spatial frequency and W (ω) is defined for each filter as Ram-Lak filter: rect (ω/2), Shepp–Logan filter: multiplies the Ram-Lak filter by a sinc function, sinc (ω/2), Cosine filter: multiplies the Ram-Lak filter by a Cosine function, cos (ω/2), Hamming filter: multiplies the Ram-Lak filter by a Hamming window, 0.54 + 0.46 cos (ω), Hann filter: multiplies Ram-Lak filter by a Hann window, (0.5 + 0.5 cos (ω).

The frequency response of each filter as a function of amplitude is given in Fig. 1 [13]. Image quality analysis was performed using ImageJ software (National Institute of Health, USA). The various tests performed and the Catphan modules involved in these tests are given below.

Fig. 1
figure 1

Frequency response curves for various reconstruction filters

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Pixel stability

The reconstructed CTP 404 module of the Catphan was used to assess the pixel value stability for each of the inserts. The mean and standard deviations (SD) of seven different inserts were computed. Ideally, the mean value computed is indicative of HU values and the standard deviation represents noise (σ) in that region.

HU uniformity

The CTP 486 module of the Catphan containing a homogenous material was used to quantify the image uniformity. The mean HU values over the area defined by ROIs on central and four peripheral regions on the same slice of the Catphan image (Fig. 2) were measured to evaluate the uniformity of the image. The stability of pixel values from the peripheral region to the center of an image slice defines the image uniformity. Thus the image uniformity [2] is evaluated using the Uniformity Index (UI) from Eq. 2.

$${\text{UI }} = \frac{{{\text{HU}}_{\text{periphery }} - {\text{HU}}_{\text{center}} }}{{{\text{HU}}_{\text{center}} }} \times 100$$
(2)
Fig. 2
figure 2

CTP 486 module of Catphan with ROIs drawn

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If the UI is positive, this is indicative of the “cupping” artefact; if the UI is negative, then it would indicate the “capping” artefact. Profiles generated over the uniform section of the Catphan for two different modes of CBCT acquisition were analysed for image uniformity.

CNR

CNR is defined as the difference between the average HU values in the insert and background, divided by average noise [3]. In this study, CNR is calculated for the acrylic insert according to Eq. 3.

$${\text{CNR}} = 2 \times \frac{{| {{\text{HU}}_{\rm{insert }} - {\rm{HU}}_{\rm{background}} }|}}{{{{\sigma }}_{\rm{insert}} + {{\sigma }}_{\rm{background}} }}$$
(3)

Spatial resolution

The CTP 528 module containing 1 through 21 line pairs/cm was used to evaluate the spatial resolution. The Modulation Transfer Function (MTF) which represents a measure of the spatial resolution in the imaging system was evaluated according to the method outlined by Droege and Morin [14]. In this study the MTF was measured based on the change of density across each line pair pattern using Eq. 4 as,

$${\text{MTF}} = \frac{{\frac{{{\pi }}}{{\sqrt {2 } }}*\sqrt {{\text{M}}^{2} - {\text{N}}^{2} } }}{{\left| {{\text{CT1}} - {\text{CT2}}} \right|}}$$
(4)

where, M: SD of pixel value within line pair pattern; N: SD of noise in the uniform region of the image; CT1 and CT2: are the mean pixel values across two areas of different thickness or density in the range of 10–15 %. The resolution obtainable for a given system is estimated by 50 and 10 % MTF i.e. frequency at which the contrast has dropped to 50 and 10 % of the maximum value obtained at 0 line pair/mm respectively.

Results

Pixel stability

The measured average pixel values for 0.5 cm diameter circular ROIs in various inserts of the Catphan module, CTP 404, for full-fan and half-fan modes are reported in Table 1. In general, full-fan mode measures high percentage difference of HU when compared to estimated HU values. This inconsistency in HU values is due to the deviation of reconstructed density values from the true ones during back projection. Since structures within the FOV are covered within the beam only over small angular ranges (200° gantry rotation in full-fan mode), there occurs an inconsistency in the reconstructed volume as this problem is not accounted for during back projection. However, the effect of reconstruction filters on measured HU values is not significant. Hann and the Hamming filter give the least noise with the SD reduced by more than 65 % relative to default Ram-Lak filter.

Table 1 Insert materials present in Catphan CTP 404 modules and their expected and measured HU values
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HU uniformity

The uniformity index (UI) is measured using the circular ROIs defined at the center and the periphery of the phantom. Table 2 shows the Uniformity Index measurements `on reconstructed slice of Catphan using five different filters in full- and half-fan modes. The full-fan has a UI of −4.16 % and half-fan has −2.12 % using the Ram-Lak filter which suggests differential beam hardening through the central and peripheral regions of the uniform module in both cases. This is due to the fact the cone beam image quality degrades with larger cone angles i.e. as a function of distance to the central slice. This ‘capping effect’ is more pronounced for small FOV scans (full-fan) than for large FOV scans (half-fan). With the Ram-Lak and Hamming filters, the percentage of HU difference is slightly lower when compared to other filters. In general, image uniformity is least affected by the reconstruction filters. The central profiles of the image uniformity module in the Catphan were produced using different acquisition modes and are shown in Fig. 3. The profile in the image reconstructed with higher tube current was found to stabilize with small fluctuations than the profile through the image reconstructed with lesser tube current.

Table 2 Uniformity index measurements on reconstructed slice of Catphan using five different filters in full- and half-fan modes
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Fig. 3
figure 3

Central profiles of reconstructed axial slices for full- and half-fan mode using Ram-Lak filter

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CNR

The axial slice of the Catphan reconstructed using the Ram-Lak and Hamming filters for full- and half-fan mode is shown in Fig. 4. The CNR was calculated for the acrylic insert (since it has low effective atomic number similar to water) using five different filters and is shown in Table 3. It was found that, in general, CNR increase for half-fan mode is approximately 3–4 times than that for full-fan mode. This suggests that noise decreases with increasing tube current. The Hamming filter gives the least noise with the CNR increased by 2.7 times when compared with the Ram-Lak filter and increased by 1.5–2 times when compared with Shepp–Logan, Cosine and Hann filters.

Fig. 4
figure 4

CTP 404 slice of Catphan reconstructed for full- fan (a, b) and half-fan (c, d) modes using Ram-Lak (a, c) filter and Hamming filter (b, d)

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Table 3 Summary of contrast-to-noise (CNR) measurements for (a) half-fan and (b) full-fan acquisition mode of CBCT using five different filters
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Spatial resolution

Figure 5 shows axial slices of the reconstructed CTP 528 module with line pairs using different filters. MTF measurements using five different filters for full- and half-fan modes are shown in Table 4. It was found that the spatial resolution of the image at 10 % MTF was decreased by 25 % when the tube current is increased by four times from full-fan mode (for head protocol) to half-fan mode (for Pelvis protocol).

Fig. 5
figure 5

CTP 528 slice of Catphan reconstructed using (a) Ram-Lak, (b) Hamming filter, (c) Shepp–Logan, (d) Cosine and (e) Hann filters showing the number of line pairs seen

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Table 4 Summary of the MTF measurement for CBCT imaging system using five different reconstruction filters. The frequencies at which the MTF are 0.5 and 0.1 are shown
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The relation between MTF and line pairs per centimeter for five different reconstruction filters for half-fan and full-fan modes are shown in Fig. 6a, b respectively. In both full-fan and half-fan modes, at 50 % MTF, the number of line pairs measured by all the filters are minimally varied (~3 lp/cm for full-fan and ~2 lp/cm for half-fan). However, at 10 % MTF, the variation in spatial resolution is quite high. In half-fan mode, maximum spatial resolution was given by the Ram-Lak filter (~6 lp/cm) and minimum (~4 lp/cm) by the Hann. In full-fan mode, at 10 % MTF, the maximum line pairs seen using the Ram-Lak is 8 lp/cm and minimum is seen using the Hann filter (6 lp/cm). This indicates that spatial resolution is influenced by the reconstruction filter and hence the spatial resolution can be improved by using a filter that emphasizes high-frequency components.

Fig. 6
figure 6

MTF calculated for (a) half-fan mode and (b) full-fan mode

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Discussion and conclusion

Kilovoltage CBCT enables acquisition of 3D images of the patient before treatment that can be directly compared with planning CT images for verifying the patient set-up: so-called ‘Image-Guided Radiotherapy’ (IGRT). Another possibility is to use CBCT to perform ART, where image contouring, treatment planning and dose computation is performed using cone beam images. However, reliable contouring of tumor volumes and organs at risk requires acceptable image quality. In this study, the image quality parameters of the Varian CBCT imaging system were evaluated in a quantitative way to assess the optimum acquisition mode and reconstruction filters to be used on volumetric imaging protocols. The low-contrast resolution of an image, which distinguishes between materials of similar densities, is not studied as this depends on the reconstructed thickness of the slice.

For the studied CBCT system, the HU variation and SD is high for full-fan mode, indicating a higher noise level due to lower tube current. Comparing all five filters, the Hamming and Hann filter seems to be the most optimal for noise reduction as they provide the least variation (<5 %) in the average pixel values with CNR increased by a factor of 2.7 compared to other filters. The SD of pixels is reduced by 67 % compared to the Ram-Lak as this filter emphasizes high frequencies making it sensitive to noise. However, the spatial frequency response using the Hamming and Hann filters is very low for high frequency components as they eliminate the high frequency noise components. Comparing all the five filters used, the spatial resolution at 10 % MTF (f0.1) given by the Ram-Lak is the highest and that given by the Hann is the lowest. In half-fan mode, spatial resolution at 10 % MTF given by the Ram-Lak filter was 16 % higher than that given by the Hamming filter whereas for full-fan mode there is a significant increase of 47.5 %. Thus the number of projections has a significant effect on image noise (Fig. 3) but less influence on the spatial resolution. These findings show that we can improve different aspects of image quality by using different reconstruction filters and this can be used to our advantage for different treatment sites. For IGRT purposes, for example, in a head and neck study where positioning can be performed using bony anatomy, the need for soft tissue contrast is often not required. Thus one can opt for a Ram-Lak filter that gives improved spatial resolution. For studies that are based on soft tissue anatomy, one can opt for a filter that gives high contrast images with acceptable resolution. Adaptive radiotherapy has been introduced to account for positional variation and the tumour variation during the course of radiotherapy by modifying the tumour margin and the treatment dose based on the current patient anatomy. To achieve optimal results with ART, high spatial resolution is required for non-rigid registration of CBCT with planning CT images. Image noise and spatial resolution are two important characteristics of an image and the choice of reconstruction filter is a trade-off between the two depending upon the application. Therefore, it is important to optimize the reconstruction parameters in CBCT applications as the results show that the image quality can be improved by using appropriate reconstruction filters.