2.1

Clinical Data Preparation

For the clinical dataset, we selected raw projection data from a total of 40 clinical CT scans from different patients. The scans covered different body regions such as head, thorax and abdomen and were acquired with Somatom Flash and Somatom Force dual source CT scanners (Siemens Healthineers, Forchheim, Germany) with zFFS enabled. The dataset was split into two disjoint subsets so that 32 of the scans were used as training dataset and 8 scans served as validation dataset. It was ensured that the different body regions and CT systems used in the images were equally distributed in both datasets. Before training, some preprocessing steps were performed, i.e. instead of using the complete projection data of the scans as a whole, randomized image patches were generated to simplify the training process.

2.2

Synthetic Data Preparation

In addition to the clinical dataset, the acquisition of synthetic data for training the RIDL network was investigated. An advantage of using synthetic data would be that any number of data could be generated without requiring a CT scanner with zFFS. For the simulation we used the software package CT_SIM which is based on the deterministic ray propagation simulation software Deterministic Radiological Simulation (DRASIM). These tools allow to simulate the radiation properties in a defined X-ray imaging setup through geometrically defined phantoms.⁸ In our first experimental setup, we generated two-dimensional projection data of a water cylinder (length: 10 cm, diameter: 40 cm, density: 1.0 g/cm³) containing overlapping water spheres with varying densities (0.5 - 3.0 g/cm³) and diameters (1 - 20 cm). Each water sphere was overlaid with another, smaller water sphere of density 1.0 g/cm³, resulting in narrow circular edges with a width of 0.3 to 2 mm. These structures are particularly difficult to interpolate. Figure 2 shows an example representation of a projection from the synthetic dataset. A total of 200,000 projections with 80 detector rows and 800 channels containing randomly arranged water spheres were simulated. Comparable to real clinical projection data acquired with zFFS, the detector rows were simulated overlapped. No noise was added to the data. The dataset was split into a training dataset with 160,000 projections and a validation dataset with 40,000 projections. In addition, the range of values of the synthetic projection data was linearly scaled to the value range of the clinical data. Similar to the clinical dataset, random image patches were selected from the projection data for network training, as we will describe in more detail below.

Figure 2.

Example projection from the synthetic dataset with different sized water spheres consisting of 80 overlapped detector rows and 800 channels.

2.3

Row Interpolation with RIDL-CNN

In the previous approach of our work, a neural network was trained that received raw projection data and generated a prediction of the input with interpolated rows to effectively double the number of rows. The clinical projection data used to train the network were obtained after the rebinning, which is the rearrangement of the measured fan-beam data to parallel beam geometry. These projections were then divided into alternative rows so that projections containing all rows (acquired with zFFS) were used as the desired output y, and every other row from the corresponding projections was used for the network input x in training. In order to predict an upsampled version of the input data using the network, a so-called subpixel convolutional layer⁹ was used, which essentially performs an upsampling of the generated feature maps within the network by a specific type of image reshaping. However, this procedure is time-consuming in network training, as well as in the subsequent use of the trained network for the prediction of rows.

In further experiments, we could observe that a much simpler convolutional neural network without subpixel convolution is able to produce results comparable to the RIDL-SRResNet. In the following, we will refer to this network architecture as RIDL-CNN. Similar to the previous architecture, random patches with the size of 64×32×1 pixels were generated from the underlying projection data to train the network. Also in this case, every other row from these patches serves as network input so that it has a size of 32×32×1. The desired output has the same dimension and is obtained from the intermediate rows in the generated patches. Before network training, all patches were linearly normalized to a value range in the interval from 0 to 1. Slope and offset were set according to the minimum and maximum value of the clinical dataset. After network prediction, the input and output rows have to be interlaced to obtain corresponding interpolated projections. Furthermore, the value range of these projections must be denormalized to the original range of the clinical data. In total, the RIDL-CNN consists of an input layer followed by 12 convolutional layers with 128 filters and 3×3 kernels. The network output is computed by a final convolution. The number of trainable parameters is 1,625,857.

2.4

Implementation and Training

The RIDL-CNN was trained on both the clinical and synthetic dataset, resulting in two separately trained networks. For both datasets, 500,000 examples were selected from the corresponding training dataset and 125,000 from the corresponding validation dataset. For the training we used the Adam optimizer and a combined loss function that is described by:

This loss function was proposed in Ref. 10 and takes into account the pixel-wise computed error between the network output ŷ and ground truth y by the mean absolute error (MAE) but also the structural similarity between the two images by the multi-scale structural similarity index (MS-SSIM). The weighting factor was empirically determined as α = 0.84. The networks were trained with a batch size of 256 and an initial learning rate set to 1×10⁻⁵, which was halved if the error could not be minimized for 25 consecutive epochs.

2.5

Evaluation and Validation

In order to evaluate and validate the results, two scans of a skull phantom with real human bones were acquired with a Somatom Force system. For the first scan, a basic scan mode with a collimation of 96×0.6 mm and activated zFFS was used. For the second scan we used a scan mode of the CT system with a collimation of 48×1.2 mm. In this mode, no zFFS can be enabled and the acquired images show very strong windmill artifacts due to the lower sampling in the z-direction. In both scans the pitch factor was set to 1, since especially scans with pitch values in this range suffer from windmill artifacts.^{2, 3} A summary for both scan settings can be found in Table 1.

Table 1.

Summary of the settings for the two scans used to evaluate and validate the results.

As in our previous work, the trained networks were applied to reconstruct these phantom CT scans. For this purpose, a plugin we developed for the Siemens-specific reconstruction software was used to adjust the raw projection data after the rebinning. In the first scan, every second row, i.e. the zFFS-generated rows were replaced by rows predicted by the RIDL networks. In addition, a reconstruction with linear interpolated rows was performed, which should correspond to an acquisition without zFFS. For all reconstructions, the error measures RMSE and SSIM were calculated in relation to the ground truth reconstruction with zFFS enabled. Since no zFFS can be used in the acquisition setting employed in the second scan, there is no ground truth data. The results in these reconstructions can therefore only be evaluated qualitatively. In this case, the number of rows in the raw data was doubled by extending them with predictions from the RIDL networks.

3.1

Scan with 96×0.6 mm Collimation

Figure 3 shows reconstructions of a specific slice with differently modeled projection raw data from the first scan. Difference images are calculated to the ground truth data acquired with zFFS. Comparing the reconstruction without zFFS to the result of the RIDL-CNN trained on the clinical dataset, only a very slight reduction of the windmill artifacts can be seen in the image domain. Furthermore, there are noisy structures noticeable in the difference image in Figure 3c in the area of the bones. However, MSE and SSIM indicate a quantitatively slightly better result compared to omitting the zFFS. Looking at the reconstruction with the network trained with synthetic data (see Figure 3d), we find an improvement in the image quality both in the image domain and in the difference image. Especially the problem with the noisy structures in the bone areas does not occur. With regard to the error measures, this reconstruction also provides the best result quantitatively.

Figure 3.

Qualitative and quantitative comparison of a reconstructed slice (1. scan) without zFFS, with the RIDL-CNN trained with the clinical dataset and the RIDL-CNN trained with the synthetic dataset compared to the ground truth scan with zFFS (C = 60 HU, W = 360 HU). Below the difference images to the ground truth are shown (C = 0 HU, W = 150 HU).

3.2

Scan with 48×1.2 mm Collimation

Figure 4 compares the results for two reconstructed slices from the second scan. In both slices reconstructed with WFBP without zFFS, very dominant windmill artifacts can be observed. Comparing these slices with the results of the network trained with clinical data, a slight reduction of the artifacts can be seen qualitatively. The results obtained with the network trained with the synthetic dataset can most effectively reduce the occurring windmill artifacts and provide superior image quality compared to the network trained with clinical data. The comparison of the reconstructions can only be performed qualitatively due to missing ground truth data, since the applied scan mode does not allow for enabling zFFS.

Figure 4.

Qualitative comparison of two selected slices (2. scan) without zFFS, with the RIDL-CNN trained with the clinical dataset and the RIDL-CNN trained with the synthetic dataset (C = 60 HU, W = 360 HU).