Low-dose CT reconstruction by self-supervised learning in the projection domain

Inspire by Noise2Context[22] and Noise2Stack[16], we composed above two methods and reconstructed our model, Noise2Projection. Because there are over 1000 projections in one rotation of our CT scan, the variations between neighbouring projection data are minimal. As a result, this model for projection data is being considered in order to reduce noise and increase the quality of reconstructed CT images. We use the projection data of three consecutive angles as the model’s input and estimate the projection data of the intermediate angles, as indicated in Fig.1.

For LDCT denoising in the projection domain, the basic mathematical model can be formulated as: $y=x+n$, $y$ is the noisy LDCT projection image, $x$ is the corresponding clear reference, $n$ denotes the noise. To obtain clean LDCT projection image from $y$, a neural network $F_{\theta}$ can be trained with object function as in Eq.1:

In our model, we use the projection data of three adjacent angles ($y^{k}_{s-1}$,$y_{s}^{k}$ and $y_{s+1}^{k}$) as the input to the model and estimate the projection data of the intermediate angles. Since there is no corresponding clean projection images, we use a self-supervised learning method to train our model. The objective function of our network is Eq. 2.

Where $y_{s}^{k}$, $y_{s-1}^{k}$, and $y_{s+1}^{k}$ are three adjacent projection data of the $k$th patient, $s$ is the index of projection image.

Similar to the [22], we make the following assumptions: (a) the differences in projection data of adjacent angles are minor; (b) the noise in projection data of distinct projection angles is independent of each other and zero mean. Under those assumption, $\left|\left|F_{\theta}(y_{s}^{k})-y_{s-1}^{k}\right|\right|_{2}^{2}+\left|\left|F_{\theta}(y_{s}^{k})-y_{s+1}^{k}\right|\right|_{2}^{2}$ is equal to $2*\left|\left|F_{\theta}(y_{s}^{k})-x_{s}^{k}\right|\right|_{2}^{2}$. As a consequence, Eq. 2 and Eq. 1 are equivalent.

We can observe from Eq.2 that if we employ the adjacent two slices and itself as the supervision, the unsupervised problem is equal to having the ground truth as the supervision under specific assumptions.

Because our method is a training strategy rather than an architectures per se, it may be used to any acceptable neural network backbone. In this work, to implement our Noise2Projection, we use standard U-net [17] with 32 basic feature-maps as the primary neural network, $F$, and Eq. 2 as the loss function.

We trained our model by using clinical human chest CT scan datasets. A total of 10 clinic patient(range 44.3-103kg) CT scan data were taken by the Minfound ScintCare CT16 scanner, and we randomly selected 7, 1 and 2 patients data for training, validation and testing, respectively. The number of projection views for a full 360^∘ rotation is 1024 and the dimension of each acquired projection image is 912$\times$16. On average, each patient has 17741 projections. During the projection data acquisition, the x-ray tube current was set at 30 mA, and the duration of the x-ray pulse at each projection view was 15 ms. The tube voltage was set to 120 kVp. The reconstruction was performed using the manufacturer-provided software with all physical corrections. The size of each reconstructed CT image is 512$\times$512 with pixel size of 0.706*0.706mm. Because a scan circle has 1024 projections, the difference between consecutive projection data is quite modest. In Fig.  2, 10 consecutive CT projections are shown, with no noticeable structure change.

In this work, we implement Noise2Projection and one unsupervised model (CycleWGANs [23]) in image domain as a baseline. The unsupervised baseline is trained with the same loss function as in the original paper [23], but without the supervised learning loss, just adversarial loss ($\mathcal{L}_{adv}$), consistency loss ($\mathcal{L}_{cyclic}$), and cyclic loss ($\mathcal{L}_{identity}$) are included.

The denoising network was built in Keras with Tensorflow backend and tested on NVIDIA GeForce RTX 3090 GPUs. The neural networks were initialized with a normal distribution and trained by Adam optimizer with with $\beta_{1}$ =0.5 and $\beta_{2}$=0.999 during 100 epochs. The learning rate was set at $2\times 10^{-4}$ and decremented linearly to zero. For training, the batch size was set to 16 and for inference, it was set to 1. The network uses full size $912\times 16$ projections image for end-to-end processing for training and inference.

No NDCT images can be utilized as a reference because our dataset was obtained from a clinical setting. In the CT image domain and projection domain, the noise reducation ratio, Z-profile, profile, and human vision sanity check were employed to assess model performance.

Fig. 3(a) shows a comparison of the raw and Noise2Projection processed projection images. Because the projected image’s height is only 16 pixels, it’s tough to see the details, but the difference between the two may be seen. The Noise2Projection model predicts a decreased noise level in the projection data and no change in the local structure, as shown in Fig. 3(a).

The Z-profile (The mean value of each slice along the Z-direction) of raw and Noise2Projection processed projection data are shown in Fig. 3(b). Due to low-dose CT scan, the number of photon passing through the body is lower than NDCT scan and resulting noise projection data. The noise in Noise2Projection model estimated data is lower than the raw projection data (smaller fluctuation in Z-profile), and the quantitative inaccuracy is almost non-existent (relative error is less than 0.01% )

Our Noise2Projection model first processes the raw projection data, then we import the processed projection data along with the raw projection data into the CT vendor’s reconstruction tool for image reconstruction, and finally we assess the quality of the reconstructed images using quantitative and qualitative methods.