Unsupervised Denoising in Spectral CT: Multi-Dimensional U-Net for Energy Channel Regularisation

Abstract

Spectral Computed Tomography (CT) is a versatile imaging technique widely utilized in industry, medicine, and scientific research. This technique allows us to observe the energy-dependent X-ray attenuation throughout an object by using Photon Counting Detector (PCD) technology. However, a major drawback of spectral CT is the increase in noise due to a lower achievable photon count when using more energy channels. This challenge often complicates quantitative material identification, which is a major application of the technology. In this study, we investigate the Noise2Inverse image denoising approach for noise removal in spectral computed tomography. Our unsupervised deep learning-based model uses a multi-dimensional U-Net paired with a block-based training approach modified for additional energy-channel regularization. We conducted experiments using two simulated spectral CT phantoms, each with a unique shape and material composition, and a real scan of a biological sample containing a characteristic K-edge. Measuring the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) for the simulated data and the contrast-to-noise ratio (CNR) for the real-world data, our approach not only outperforms previously used methods-namely the unsupervised Low2High method and the total variation-constrained iterative reconstruction method-but also does not require complex parameter tuning.

Keywords: deep learning; spectral computed tomography; unsupervised denoising method.

Figure 1

Our approach: The spectral sinograms are obtained over ${360}^{\circ }$ and split into 4 $(K=4)$ mutually exclusive sets, which are reconstructed independently for each energy channel using FBP. The network is trained using images generated by averaging all possible combinations of 3 reconstructions out of the 4 images as network input to predict the 4th spectral image not used to generate the current network input. Once trained, all 4 images are averaged and denoised by the model. The workflow is divided into three main stages, each distinguished by a unique colour.

Figure 2

(a) Source spectrum obtained with SpekPy at 150 kVp. The source spectrum has a maximum value of $5.58\times {10}^7{\mathrm{photons}/\mathrm{cm}}^2/\mathrm{mAs}/\mathrm{keV}$, representing the peak fluence per unit of energy. (b) Normalised X-ray source spectrum over the energy range of 20 to 150 keV. The y axis represents the number of photons, while the x axis indicates the energy level in keV for both spectra.

Figure 3

Examples of phantoms at energy levels of $45\mathrm{keV}$ and $70\mathrm{keV}$, featuring different materials and shapes: (a) water, olive oil, nitromethane, and acetone; (b) methanol, ethylenediamine, aluminium, and nitrobenzene.

Figure 4

Channel-wise reconstruction for the first phantom. The first column is the ground truth, and the second column is the noisy reconstruction with FBP. The third column represents the iterative reconstruction method, and 1 indicates the alpha value selected for TV minimisation. The fourth column shows our method, and the last column shows the unsupervised Low2High method.

Figure 5

Channel-wise reconstruction for the second phantom. The first column is the ground truth, and the second column is the noisy reconstruction with FBP. The third column represents the iterative reconstruction method, and 0.5 indicates the alpha value selected for TV minimisation. The fourth column shows our method, and the last column shows the unsupervised Low2High method.

Figure 6

Comparative analysis using PSNR and SSIM metrics of synthetic data. These metrics are evaluated across the entire image. (a) Channel-wise PSNR for the first phantom; (b) channel-wise SSIM for the first phantom; (c) channel-wise PSNR for the second phantom; (d) channel-wise SSIM for the second phantom.

Figure 7

Examples of the linear attenuation coefficient of different materials over the energy channels for the synthetic data. Both axes are shown on a logarithmic scale, with tick marks manually adjusted for clarity. (a) Water; (b) nitromethane; (c) methanol; (d) aluminium.

Figure 8

Reconstruction result of iterative methods at energies of (a) 25 keV and (b) 35 keV. The first column represents the reconstruction with full projection using FDK. The other three columns show the iterative reconstruction method, the numbers in the headings indicate the alpha values selected for TV minimisation.

Figure 9

Reconstruction result of of all methods at energies of (a) 25 keV and (b) 35 keV. The first column represents the reconstruction with full projection, and the second column represents the reconstruction with half projection using FDK. The third column represents the iterative reconstruction method, and 0.035 indicates the alpha value selected for TV minimisation. The fourth column shows our method, and the fifth column shows the unsupervised Low2High method.

Figure 10

Attenuation profile across energy levels for the selected area from the lens in the biological sample. The coloured line signifies the K-edge of iodine at 33.169 keV. (a) All methods; (b) iterative methods; (c) calculations of CNR across channels for the iodine-stained jaw of the biological sample.

Figure 11

Three-dimensional visualisation of the biological sample. The image on the left depicts a 3D spatial visualisation of the biological sample reconstructed with IR-TV for an energy channel. The remaining images show a spatial 2D image slice, with the third dimension showing the energy channels for the reconstructions obtained by FDK, IR-TV, and our approach, respectively. The K-edge in the energy spectrum is shown with a red arrow, ROI’s are indicated by a white arrows. The y axis in the latter images represents the energy dimension.