1. Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2. Lanzhou University, Lanzhou 730000, China
3. Jiangsu Institute of Metrology (Jiangsu Energy Measurement Data Center), Nanjing 210023, China
4. Nanjing Tech University, Nanjing 211816，China
Abstract：The energy spectrum of X-rays plays a critical role in computed tomography (CT) applications. Accurate spectral information is crucial for implementing spectral CT and effectively correcting artifacts resulting from beam hardening in conventional CT reconstruction. In the fields of medical imaging and industrial inspection, high-power X-ray tubes are commonly used due to their ability to produce a large flux of X-rays in a short time, thereby improving imaging efficiency and enabling the acquisition of high-resolution and high-contrast images. However, directly measuring the energy spectrum of high-power X-ray tubes becomes challenging due to their excessively high photon flux.Currently, energy spectrum estimation is the predominant method for obtaining spectral information. This approach involves acquiring projection data from phantoms of varying thicknesses and establishing a system of equations that relate the spectrum, attenuation coefficients, and projection data. By solving this system, the energy spectrum can be obtained. However, the accuracy of this method relies heavily on the precision of algorithms and data. Due to the severely ill-posed nature of the equations, the reconstructed spectrum often lacks critical spectral features when suitable initial values are not provided. To address this limitation, this study proposes a novel method that combines direct measurement with neural network-based prediction. The photon flux of the X-rays is reduced to a detectable level by introducing a certain thickness of iron filters. A series of spectral data is then acquired by sequentially adding thin iron filters of varying thicknesses. These data are used to train a neural network model, enabling precise prediction of the emitted energy spectrum. Simulation results demonstrate the outstanding performance of the proposed neural network model in predicting energy spectra, achieving a root mean square error (RMSE) of only 0.000 031 between the normalized predicted spectrum and the ground truth. However, due to experimental limitations, the amount of measured data is relatively small. To enhance the model's generalizability and prediction accuracy, this study integrates transfer learning. Specifically, a neural network is first trained on a large dataset generated using GEANT4 simulations, and then fine-tuned using a small amount of experimentally measured spectral data. Prediction results based on experimental data show an RMSE of 0.000 194 between the normalized predicted spectrum and the ground truth. Compared to traditional spectral estimation methods, the proposed approach not only achieves significantly higher accuracy but also effectively captures critical spectral features. The advantages of this method lie in leveraging the powerful learning capabilities of neural networks, thereby overcoming the dependency on initial values and ill-posed equation solving in traditional methods, and greatly improving prediction stability and accuracy. Both simulation and experimental results validate the feasibility of the proposed approach.
Key words：Energy spectrum measurement; CdTe detector; Neural networks; Transfer learning
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