Title: Self-supervised regression learning using domain knowledge: Applications to improving self-supervised image denoising. Abstract: Regression that predicts continuous quantity is a central part of applications using computational imaging and computer vision technologies. Yet, studying and understanding self-supervised learning for regression tasks -- except for a particular regression task, image denoising -- have lagged behind. This paper proposes a general self-supervised regression learning (SSRL) framework that enables learning regression neural networks with only input data (but without ground-truth target data), by using a designable operator that encapsulates domain knowledge of a specific application. The paper underlines the importance of domain knowledge by showing that under some mild conditions, the better designable operator is used, the proposed SSRL loss becomes closer to ordinary supervised learning loss. Numerical experiments for natural image denoising and low-dose computational tomography denoising demonstrate that proposed SSRL significantly improves the denoising quality over several existing self-supervised denoising methods.