## 3 Methodology
### Dropped Projection Strategy  
In the natural image domain, the blind spot strategy reduces noise by restoring the signal from the Bernoulli-sampled instances of the input image. The blind spot strategy defines the pixels in the input image as follows:  
\[x_{i}=s_{i}+n_{i}, \tag{12}\]  
where \(s_{i}\) denotes the signal of the \(i\)th pixel that is pixel-wise dependent and \(n_{i}\) denotes the noise of the \(i\)th pixel that is pixel-wise independent. The blind spot strategy uses Bernoulli sampling to remove the \(x_{i}\), which is the \(i\)th pixel of the input image, and restores \(s_{i}\) from the adjacent pixels. A denoising neural network is trained using the blind spot strategy by solving  
\[\operatorname*{argmin}_{\theta}\sum_{i}L\big{(}f\big{(}x_{i}^{\prime},\theta \big{)},x_{i}\big{)}, \tag{13}\]  
where \(x_{i}^{\prime}\) is the Bernoulli-sampled instance of the input image and \(L(\cdot)\) denotes the L2 loss. This approach has demonstrated promising results in the natural image domain. However, for the mentioned reason, another approach is needed to reduce the noise of the LDCT reconstructed images. Therefore, we propose a strategy to generate the Bernoulli-sampled instance of the projection image and restore it in the reconstructed image domain. The diagram of the proposed method is presented in Figure 3.  
To reduce the noise in the reconstructed image domain using the blind spot strategy, we must generate the input images of the denoising neural network in which the independent  
Figure 3: Flowchart of the proposed method with the dropped projection strategy (_DPS_). In the training phase, we map each slice of the reconstructed image (reconstructed using dropped projection images) to each slice of the reconstructed image (reconstructed by non-dropped projection images).  
noise is removed. According to Equation (11), photon noise in the projection image is ramp-filtered and integrated into the reconstructed image along the ray. Thus, we must remove the pixels of the projection image to generate the projection image in which the independent noise is removed using Bernoulli sampling. The Bernoulli-sampled projection image \(q^{\prime}\) can be defined as follows:  
\[q^{\prime}=(\hat{q}*g_{\infty})\ \odot\ b\, \tag{14}\]  
where \(\odot\) represents the element-wise multiplication and \(b\) denotes the binary Bernoulli vector with elements 1 and 0, which are randomly generated. The binary Bernoulli vector \(b\) can be expressed as follows:  
\[b=\left\{\begin{array}{ll}1&\quad\text{with probability }k,\\ 0&\quad\text{with probability }1-k,\end{array}\right. \tag{15}\]  
where the probability \(k\) has a value from 0 to 1. Therefore, we can generate the 3D image \(f^{\prime}\) reconstructed from the Bernoulli-sampled projection image \(q^{\prime}\). Using Equations (11) and (14), \(f^{\prime}\) is defined as follows:  
\[\begin{array}{ll}f^{\prime}(x,y)&=\frac{2\pi}{N_{0}}\sum_{i=0}^{N_{0}-1}(( \hat{q}*g_{\infty})\odot b)[i,ycos\theta-xsin\theta]\\ &=\frac{2\pi}{N_{0}}\sum_{i=0}^{N_{0}-1}q^{\prime}[i,ycos\theta-xsin\theta]. \end{array} \tag{16}\]  
We can generate blind spots in the reconstructed image \(f^{\prime}\) using this method.