  Noise is ubiquitous during image acquisition. Sufficient denoising is often
an important first step for image processing. In recent decades, deep neural
networks (DNNs) have been widely used for image denoising. Most DNN-based image
denoising methods require a large-scale dataset or focus on supervised
settings, in which single/pairs of clean images or a set of noisy images are
required. This poses a significant burden on the image acquisition process.
Moreover, denoisers trained on datasets of limited scale may incur
over-fitting. To mitigate these issues, we introduce a new self-supervised
framework for image denoising based on the Tucker low-rank tensor
approximation. With the proposed design, we are able to characterize our
denoiser with fewer parameters and train it based on a single image, which
considerably improves the model's generalizability and reduces the cost of data
acquisition. Extensive experiments on both synthetic and real-world noisy
images have been conducted. Empirical results show that our proposed method
outperforms existing non-learning-based methods (e.g., low-pass filter,
non-local mean), single-image unsupervised denoisers (e.g., DIP, NN+BM3D)
evaluated on both in-sample and out-sample datasets. The proposed method even
achieves comparable performances with some supervised methods (e.g., DnCNN).
