Xuan Liu

Risheng Liu, Xuan Liu, Shangzhi Zeng et al.

In recent years, by utilizing optimization techniques to formulate the propagation of deep model, a variety of so-called Optimization-Derived Learning (ODL) approaches have been proposed to address diverse learning and vision tasks. Although having achieved relatively satisfying practical performance, there still exist fundamental issues in existing ODL methods. In particular, current ODL methods tend to consider model construction and learning as two separate phases, and thus fail to formulate their underlying coupling and depending relationship. In this work, we first establish a new framework, named Hierarchical ODL (HODL), to simultaneously investigate the intrinsic behaviors of optimization-derived model construction and its corresponding learning process. Then we rigorously prove the joint convergence of these two sub-tasks, from the perspectives of both approximation quality and stationary analysis. To our best knowledge, this is the first theoretical guarantee for these two coupled ODL components: optimization and learning. We further demonstrate the flexibility of our framework by applying HODL to challenging learning tasks, which have not been properly addressed by existing ODL methods. Finally, we conduct extensive experiments on both synthetic data and real applications in vision and other learning tasks to verify the theoretical properties and practical performance of HODL in various application scenarios.

Risheng Liu, Xuan Liu, Shangzhi Zeng et al.

Recently, Optimization-Derived Learning (ODL) has attracted attention from learning and vision areas, which designs learning models from the perspective of optimization. However, previous ODL approaches regard the training and hyper-training procedures as two separated stages, meaning that the hyper-training variables have to be fixed during the training process, and thus it is also impossible to simultaneously obtain the convergence of training and hyper-training variables. In this work, we design a Generalized Krasnoselskii-Mann (GKM) scheme based on fixed-point iterations as our fundamental ODL module, which unifies existing ODL methods as special cases. Under the GKM scheme, a Bilevel Meta Optimization (BMO) algorithmic framework is constructed to solve the optimal training and hyper-training variables together. We rigorously prove the essential joint convergence of the fixed-point iteration for training and the process of optimizing hyper-parameters for hyper-training, both on the approximation quality, and on the stationary analysis. Experiments demonstrate the efficiency of BMO with competitive performance on sparse coding and real-world applications such as image deconvolution and rain streak removal.

Xuan Liu, Yaoqin Xie, Jun Cheng et al.

Denoising low-dose computed tomography (CT) images is a critical task in medical image computing. Supervised deep learning-based approaches have made significant advancements in this area in recent years. However, these methods typically require pairs of low-dose and normal-dose CT images for training, which are challenging to obtain in clinical settings. Existing unsupervised deep learning-based methods often require training with a large number of low-dose CT images or rely on specially designed data acquisition processes to obtain training data. To address these limitations, we propose a novel unsupervised method that only utilizes normal-dose CT images during training, enabling zero-shot denoising of low-dose CT images. Our method leverages the diffusion model, a powerful generative model. We begin by training a cascaded unconditional diffusion model capable of generating high-quality normal-dose CT images from low-resolution to high-resolution. The cascaded architecture makes the training of high-resolution diffusion models more feasible. Subsequently, we introduce low-dose CT images into the reverse process of the diffusion model as likelihood, combined with the priors provided by the diffusion model and iteratively solve multiple maximum a posteriori (MAP) problems to achieve denoising. Additionally, we propose methods to adaptively adjust the coefficients that balance the likelihood and prior in MAP estimations, allowing for adaptation to different noise levels in low-dose CT images. We test our method on low-dose CT datasets of different regions with varying dose levels. The results demonstrate that our method outperforms the state-of-the-art unsupervised method and surpasses several supervised deep learning-based methods. Codes are available in https://github.com/DeepXuan/Dn-Dp.