## 1 Introduction
Although these methods have exhibited superior performance in the natural image domain, they are challenging to apply to noise reduction in reconstructed LDCT images because of the propositions in the blind spot strategy. The methods using the blind spot strategy have two simple statistical propositions: (1) the signal is not pixel-wise independent, and (2) the noise is pixel-wise independent. The methods that use the blind spot strategy perform noise reduction correctly when satisfying these propositions. Deep learning-based noise reduction approaches in LDCT can be divided into the following types: noise reduction in the reconstructed image domain and noise reduction in the projection or sinogram domain. The noise caused by an insufficient radiation dose is photon noise with a Poisson distribution. Photon noise can be treated as pixel-wise independent in projection images. However, the reconstructed image is created by reconstructing the signal of the plurality of the projection image. Thus, the noise in the reconstructed image is not pixel-wise independent. Because of this phenomenon, if a blind spot strategy-based noise reduction technique is performed on reconstructed data, artifacts caused by photon noise are recognized as structures, emphasizing them more. Figure 1 illustrates that artifacts are emphasized when the noise reduction technique with the blind spot strategy is performed in the reconstructed image domain. For these reasons, several researchers have performed noise reduction in the projection domain using the blind spot strategy [27, 28]. These approaches satisfy the assumptions of the blind spot strategy. However, in general, as projection images for LDCT have extremely weak signals compared with reconstructed images, performing noise reconstruction using projection images is a challenging task. Therefore, these approaches indicate promising results, but the over-smoothing problems, such as smoothed edges or removed microstructures, remain. In this work, we propose a self-supervised noise reduction method in LDCT that solves the mentioned problems. The proposed method can train a denoising neural network for LDCT without paired images. Like any other methods using the blind spot strategy, we make two statistical assumptions. First, the signal of the projection image is not pixel-wise independent. Second, the noise of the projection image is pixel-wise independent. We focus on reducing the photon noise of the projection image. Artifacts not caused by photon noise from the projection image (e.g., line defects in projection images, X-ray scattering, and artifacts caused by geometric misalignment) are not considered in this study. Very recently, Self2 Self [26] exhibited superior performance using the dropout-based ensemble. The dropout-based ensemble is a strategy that predicts noise-reduced images from randomly dropped images iteratively and outputs the result, which is the average of all predictions. It reduces the noise by dropping out the signal and restoring it using the signal from adjacent pixels. Motivated by work on Self2 Self, we propose a dropped projection strategy (\(DPS\)) that randomly drops the pixels from the projection images, reconstructs the 3D reconstructed image using randomly dropped projection images, and trains a denoising neural network with the reconstructed images. A denoising neural network is trained to restore the signal from the reconstructed image, which is reconstructed by dropped projection images using the \(DPS\), and allows the neural network to reduce the noise from the projection images. In this way, we overcome the problems of previous studies which have performed noise reduction in the projection domain, such as over-smoothing problems by using dropout in the projection domain and restoring it in the 3D reconstructed image. In addition, the denoising neural network using the \(DPS\) is trained to restore the signal from the pixel-wise independent noise in the projection images. This method allows noise reduction without emphasizing artifacts caused by photon noise.