## 1 Introduction
Its performance is close to that of DNNs trained on noisy-clean pairs. Subsequently, Noise2 Void [16] and Noise2 Self [17] were proposed to train DNNs using only unorganized noisy image pairs. To avoid learning identity mapping, the blind-spot networks proposed in Noise2 Void only utilize the neighboring pixels to predict each pixel. Similarstrategies were used in the parallel work of Noise2 Self. Although Noise2 Noise, Noise2 Void, and Noise2 Self achieved good denoising results, the noisy images used for model training were heavily correlated to the observed noisy image. Collecting such noisy images is also challenging and costly in practice. Unlike blind-spot methods, the training pairs used in Noisier2 Noise [18] and Noisy-as-Clean [19] are generated by adding synthetic noise to the observed noisy image. However, it is difficult to specify a noise-generating model for real-world scenarios. Similar to Noiser2 Noise and Noisy-as-Clean, R2R [20] corrupts noisy images with specific noise levels to generate training pairs. However, prior knowledge of the noise levels required in R2R is difficult to collect in real-world scenarios. Another method, Self2 Self [21], proposed a dropout denoiser that was trained on Bernoulli sampled noisy image pairs. Self2 Self generates multiple recovered images and uses the average of the recovered images as the final reconstructed result. This method has achieved better performance in real-world image denoising; however, it still cannot handle low-illumination images. To improve denoising performance, Neighbor2 Neighbor [22] constructs a noisy pair by subsampling a given noisy image. However, its performance still relies heavily on a large-scale training dataset to a great extent. In contrast to the aforementioned unsupervised image-denoising methods, deep image prior (DIP) [23] has received much attention. DIP adopts a generator network to capture low-level image statistics prior without the need for pretraining or additional data. The network parameters were optimized by considering the given noisy image as the learning target with a random noise input. Although the DIP demonstrated that the trained DNN can represent a well-recovered image, its performance is relatively weak compared with state-of-the-art supervised methods, especially for synthetic image denoising. The main reason for this is that the image quality of the DIP learning target is relatively low, which leads to a large search space and slow convergence. Moreover, the two DIP learning methods cannot generate identical denoised images even given the same network input and the same targeting noisy image due to the randomly initialized network weights. For different noisy images, the reconstruction processes lead to more diverse recovery results. In this study, aiming at improving the denoising performance of DIP, we propose a two-stage unsupervised image denoising framework that achieves better performance than state-of-the-art supervised models. In contrast to DIP, which generates only one denoised image, we try to reconstruct a set of intermediate denoised images across the image space using multiple DIP learning processes and take the fusion of the intermediate images as the final denoised image. In our study, we first propose a two-target DIP learning strategy to improve the denoising effect. A preliminary image, together with the given denoised image, is taken as a DIP learning target. Through the proposed up- and down-sampling strategy, multiple sampled images of a denoised image, which is generated by a supervised denoising method, can be obtained. These preliminary images were learned by several two-target DIP optimization processes to generate multiple intermediate denoised instances. The intermediate denoised images, which contain different recovered details, are complementary. To further improve the denoising effect, we developed an unsupervised image fusion network to generate weight maps for the intermediate denoised instances, which we used to fuse the DIP-recovered instances into a single denoised image.