  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 pseudo-predictor
that encapsulates domain knowledge of a specific application. The paper
underlines the importance of using domain knowledge by showing that under
different settings, the better pseudo-predictor can lead properties of SSRL
closer to those of ordinary supervised learning. Numerical experiments for
low-dose computational tomography denoising and camera image denoising
demonstrate that proposed SSRL significantly improves the denoising quality
over several existing self-supervised denoising methods.
