# Deep Scatter Estimation (DSE): Accurate Real-Time Scatter Estimation for X-Ray CT Using a Deep Convolutional Neural Network

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## Abstract

X-ray scatter is a major cause of image quality degradation in dimensional CT. Especially, in case of highly attenuating components scatter-to-primary ratios may easily be higher than 1. The corresponding artifacts which appear as cupping or dark streaks in the CT reconstruction may impair a metrological assessment. Therefore, an appropriate scatter correction is crucial. Thereby, the gold standard is to predict the scatter distribution using a Monte Carlo (MC) code and subtract the corresponding scatter estimate from the measured raw data. MC, however, is too slow to be used routinely. To correct for scatter in real-time, we developed the deep scatter estimation (DSE). It uses a deep convolutional neural network which is trained to reproduce the output of MC simulations using only the acquired projection data as input. Once trained, DSE can be applied in real-time. The present study demonstrates the potential of the proposed approach using simulations and measurements. In both cases the DSE yields highly accurate scatter estimates that differ by< 3% from our MC scatter predictions. Further, DSE clearly outperforms kernel-based scatter estimation techniques and hybrid approaches, as they are in use today.

## Keywords

X-ray scatter correction Artifact reduction CT Cone-beam CT (CBCT) Deep neural network Convolutional neural network## 1 Introduction

CT image reconstruction algorithms rely on the assumption that the acquired projection data correspond to the line integral over the spatial distribution of the attenuation coefficient. Scattered X-rays contributing to the measured signal lead to a violation of this assumption, and thus, to the introduction of CT artifacts [6, 9, 29]. These artifacts correspond to a degradation of image quality and impair dimensional measurements [12, 13]. Especially, in case of high scatter-to-primary ratios, apropriate scatter correction is crucial to avoid a loss of accuracy of the metrological assessment.

Several approaches have been proposed to address this issue. In general, they can be divided into two classes: scatter suppression and scatter estimation approaches which are the focus of this manuscript. While scatter suppression approaches try to reduce the amount of scattered X-rays reaching the detector using anti-scatter grids or collimators [26], scatter estimation approaches aim at deriving an estimate of the scatter distribution that is used to correct the acquired projection data [27]. Thereby, the scatter estimate can either be derived using dedicated hardware such as beam blockers or primary modulation grids [3, 7, 8, 20, 24, 28, 38, 39] or using software-based approaches that rely on physical or empirical models to predict X-ray scattering [1, 2, 11, 17, 18, 21, 22, 30, 32, 33, 34, 36, 37]. Among these methods the gold standard is to use a Monte Carlo (MC) photon transport code [27]. As MC is able to model all the physics of the CT acquisition process, the resulting scatter estimates are very accurate. However, the drawback of MC methods is their high computational complexity. Even highly optimized code does not perform in real-time on conventional hardware.

Thus, if computation time is an issue, so-called kernel-based models are often used in practice. These models approximate the scatter distribution by an integral transform of a scatter source term multiplied with a scatter propagation kernel [27]. Thereby, the scatter source term is usually modeled as a function of the primary intensity and reflects the probability of X-ray scattering along each ray from the X-ray source to a detector pixel. The scatter propagation kernel accounts for the spatial distribution of the scattered X-rays and depends on several parameters such as the acquisition geometry, the spectral distribution of X-rays and the object itself. Different approaches to set the scatter source term and the scatter propagation kernel have been proposed [2, 11, 14, 15, 18, 21, 23, 31, 32, 33, 34]. Basically, they can be divided into model-based and MC-based approaches. The former use a simplified theoretical model to predict X-ray scattering (for instance only forward scattering is assumed [21]) with a set of open parameters. Subsequently, the open parameters are calibrated to fit MC simulations or reference measurements. MC-based approaches, in contrast, rely on needle-beam MC simulations of slabs or ellipsoids with varying dimensions which are calculated prior to the measurement. To estimate scatter within a measured projection, one of the precalculated needle-beam kernels is assigned to every detector pixel according to an appropriate similarity metric. Finally, all kernels are summed up including correction terms that account for differences between the slabs or ellipsoids and the actual object shape.

## 2 Material and Methods

### 2.1 Kernel-Based Scatter Estimation

*G*:

*T*is usually derived from a physical model such that \(T(\psi )\) represents the probability of X-ray scattering along a ray from the X-ray source to the detector element located at \({{\varvec{u}}}\). The scatter propagation kernel

*G*with its open parameters \({{\varvec{c}}}= (c_0, c_1, \dots )\) accounts for the spreading of scattered X-rays. For a ray heading from the X-ray source to the detector element at \({{\varvec{u}}}'\), \(G({{\varvec{u}}}, {{\varvec{u}}}', {{\varvec{c}}})\) corresponds to the fraction of X-rays reaching the detector element at \({{\varvec{u}}}\). Several approaches to set

*T*and

*G*have been proposed.

*K*refers to the differential cross section of forward scattering. The scatter propagation kernel is modeled as a sum of exponential functions:

*K*as well as the open parameters \({{\varvec{c}}}\) of the scatter propagation kernel are determined by modeling them such that the scatter estimate best fits calibration measurements or the output of a MC simulation. Here, this is done by minimizing the following cost function using a simplex algorithm [19]:

*n*is the sample number, \(I_\text {s, est}\) is the scatter estimate according to Eq. (1) and \(I_\text {s}\) is a reference MC simulation.

### 2.2 Hybrid Scatter Estimation

*n*, a distinct parameter set was calculated by performing the following minimization using a simplex algorithm:

### 2.3 Deep Scatter Estimation

Conventional kernel-based models rely on simplified assumptions that do not perfectly fit arbitrary cases. Thus, their accuracy is limited and far below the accuracy of MC simulations. Furthermore it is challenging to adapt a certain model to generalize to different cases. Neural networks have the potential to overcome these drawbacks. Therefore, we propose the deep scatter estimation (DSE), a deep convolutional neural network for real-time scatter estimation. The architecture of our DSE network is shown in Fig. 1. Basically, the network is a modification of the U-net which was proposed by Ronneberger et al. for biomedical image segmentation [25]. Similar to the original model, the network consists of a downward path that plays a role at extracting a hierarchy of features from the input image and an upward path that restores the resolution of the image while transforming the features.

In order to estimate scatter, we use the forward scatter intensity as given in Eq. (2) with \(K=1\) as input to the network. Subsequently, the weights of the convolutional layers are trained to reproduce the output of a MC simulation. Thus, the network internally performs similar operations as kernel-based methods. However, in contrast to these methods, the DSE network is much more flexible since it is able to use non-linear mappings and varying scatter kernels depending on local features of the input image. Thus, DSE should model X-ray scattering more precisely and should better generalize to varying inputs.

### 2.4 Simulation Study

*w*(

*E*) is the detected X-ray spectrum that was generated according to the model of Tucker et al. [35], \(\mu (E)\) is the attenuation coefficient of the component according to the evaluated photon data library [4] and \(p({{\varvec{u}}})\) is the intersection length at detector position \({{\varvec{u}}}\) that is derived by a forward projection of the component’s CAD model. Subsequently, X-ray scatter \(I_s\) was simulated using our in-house MC simulation [1]. Finally, Poisson noise \({{\mathcal {P}}}\) was added to generate the intensity data \({\tilde{\psi }}\):

Parameters for the training and testing data of the simulation study

Training | Testing | |
---|---|---|

Detector elements | \(1024 \times 1024\) | \(1024 \times 1024\) |

Detector pixel size\(^2\) | \(0.4 \, \hbox {mm} \times 0.4 \, \hbox {mm}\) | \(0.4 \, \hbox {mm} \times 0.4 \, \hbox {mm}\) |

Source-detector distance | 1000 mm | 1000 mm |

Source-isocenter distance | 400, 500, 600 mm | 550 mm |

Tilt angle | \(0^\circ \), \(30^\circ \), \(60^\circ \), \(90^\circ \) | \(15^\circ \) |

View angle | \(360^\circ \) | \(360^\circ \) |

Tube voltage | 225, 275, 320 kV | 250 kV |

Tin prefilter | 1.0, 2.0 mm | 1.5 mm |

Scaling | 0.8, 1.2 | 1.0 |

Number of projections | 16,416 | 3600 |

### 2.5 Measurement Data

*w*(

*E*) of our system was estimated as described in Ref. [10]. Furthermore, off-focal radiation that was modeled as a convolution with an off-focal kernel \(G_\text {off}\) as described in Ref. [16] was included in the simulation. As prior for the generation of the training data, the CAD models described in Sect. 2.4 were used. However, in contrast to the simulation study, the material of all components was set to aluminum as it is not possible to penetrate steel or titanium parts with a 110 kV X-ray source appropriately. All parameters are summarized in Table 2.

Parameters for the simulated training data set and the measurement

Training | Measurement | |
---|---|---|

Detector elements | \(768 \times 768\) | \(768 \times 768\) |

Detector pixel size | \(0.388 \, \hbox {mm} \times 0.388 \, \hbox {mm}\) | \(0.388 \, \hbox {mm} \times 0.388 \, \hbox {mm}\) |

Source-detector distance | 580 mm | 580 mm |

Source-isocenter distance | 100, 110, 120 mm | 110 mm |

Tilt angle | \(0^\circ \), \(30^\circ \), \(60^\circ \), \(90^\circ \) | \(0^\circ \) |

View angle | \(360^\circ \) | \(360^\circ \) |

Tube voltage | 100, 110, 120 kV | 110 kV |

Copper prefilter | 1.0, 2.0 mm | 2.0 mm |

Scaling | 1.0 | – |

Number of samples | 8207 | 720 |

## 3 Results

### 3.1 Simulation Study

### 3.2 Measurement Data

Mean and maximum absolute percentage error between the scatter estimate and the ground truth evaluated for all 720 projection views of each component

Kernel-based | Hybrid | DSE | ||||
---|---|---|---|---|---|---|

Mean | Max | Mean | Max | Mean | Max | |

Compressor wheel | 19.8 | 84.0 | 11.7 | 61.6 | 1.46 | 13.2 |

Cylinder head | 12.4 | 66.8 | 7.2 | 36.5 | 0.63 | 10.7 |

Casting | 9.0 | 57.8 | 3.9 | 29.0 | 0.58 | 9.9 |

Bicycle cassette | 13.3 | 87.7 | 8.5 | 63.4 | 0.66 | 12.1 |

Aluminum profile | 8.8 | 30.3 | 2.7 | 16.4 | 0.78 | 5.0 |

## 4 Discussion and Conclusion

This manuscript describes the application of a deep convolutional neural network to estimate X-ray scatter in real-time. Therefore, the proposed DSE network is trained to reproduce the output of MC simulations using the acquired projection data as input. In contrast to conventional kernel-based scatter estimation approaches the DSE has the advantage of being able to use non-linear mappings and varying scatter kernels depending on local features of the input image. Thus, X-ray scattering can be modeled more precisely leading to an increased accuracy of the scatter estimates. The potential of DSE was demonstrated for simulated and measured data. The simulation study shows that the DSE generalizes well to measurements of different components with different materials and varying acquisition parameters. The performance of DSE was evaluated for cases that differed from the training data in terms of size, shape and acquisition parameters. For any of the tested components, the MAPE between the DSE scatter prediction and the ground truth was less than 1.5%. This suggests that for a practical application of DSE it is sufficient to train the network using a couple of typical cases and typical acquisition parameters. Subsequently, DSE can be applied to other cases without a major loss of accuracy. In contrast to DSE, the reference approaches showed a significantly inferior performance. The kernel-based approach led to scatter estimates with a MAPE between 8.8 and 19.8%. Also more sophisticated approaches such as the hybrid scatter estimation were less accurate (MAPE between 2.7 and 11.7%) than DSE. Especially, in regions of high attenuation the reference methods often overestimated the actual scatter distribution leading to streak artifacts within the reconstructed CT images. Similar trends can be observed for real data measured at our in-house table-top CT system. Also here, DSE clearly outperforms the two reference approaches. While CT reconstructions that were corrected using the kernel-based method and the hybrid scatter estimation show streak artifacts, DSE yields almost the same results as the MC-based correction.

However, compared to the simulation study, DSE is less accurate in case of measured data. This may be explained by the fact that the network was not trained using measurements but using simulations. Although the simulations were tuned to reproduce measurements at our CT system, they do not perfectly resemble real data. Therefore, we assume that the accuracy of the scatter estimates can be further increased if the training is performed on measured data.

It has to be noted that DSE, as it is applied here, highly relies on the accuracy of the MC simulation. If the MC code does not predict the actual scatter distribution correctly, DSE does not either. However, DSE is not restricted to reproduce MC simulations but can be trained with any other scatter estimate i.e. a scatter estimate derived using beam blockers or primary modulation approaches.

## Notes

### Acknowledgements

Parts of the reconstruction software were provided by RayConStruct^{®} GmbH, Nürnberg, Germany.

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