A contemporary survey on image reconstruction with unsupervised deep learning: from denoising to generation

Image reconstruction is fundamental for a wide range of scientific research and engineering applications such as optical imaging, biomedical imaging, and remote sensing. Mathematically, it is an ill-posed inverse problem that restores images from incomplete or perturbed measurements. Traditional methods constrain the inverse problem with analytic sparse or low-rank priors considering the sparsity and reduced dimensionality of image representation in the transformed domains and develop iterative algorithms to achieve image reconstruction. With the rise of deep learning, neural network based priors have been achieved in a data-driven manner to significantly enhance image reconstruction, and have evolved from supervised to unsupervised settings. In this paper, we provide a comprehensive overview of image reconstruction with unsupervised deep learning spanning from denoising to generation in the last decade. We interpret this trend of methods from the perspective of well-developed denoisers and bridge denoising and generative priors with the score function linking the logarithmic priors of ground truth images and their perturbed versions. They simultaneously inherit the theoretically sound property of convergence guarantees from analytic methods and enjoy the potential to be a generalized learning-based solution with reliable reconstruction performance. This paper highlights the developing trends of key methods from denoiser-based denoising priors to diffusion model based generative priors with the evolution of their core ideas and methodology characteristics. We explore existing challenges and future directions on the intersection of signal processing and machine learning for image reconstruction.