Collaborative Optimization Unfolding Networks: Prior Compensation and Proximal Mapping Augmentation for Image Compressive Sensing

Deep unfolding networks (DUNs), integrating optimization algorithms into deep neural networks, have garnered significant attention for their high performance and interpretability in image compressive sensing. However, most existing DUNs primarily focus on designing the proximal mapping operator (denoiser) while often overlooking intrinsic limitations of existing optimization models, such as the accuracy loss from the linear projection's approximate calculation and information loss between iterations. To address these problems, we propose a Prior Compensation and Proximal Mapping Augmented Unfolding Network (PCPAU-Net) for Compressed Sensing MRI (CS-MRI) reconstruction, characterized by collaboratively optimizing both the linear projection and proximal mapping stages. The Prior Compensation Module (PCM) utilizes a novel dual-domain regularization to compensate for the accuracy of linear projection outcomes, while the Proximal Mapping Augmentation (PMA) module effectively processes persistent features to minimize information loss between iterations and enhances denoising performance. Extensive CS-MRI experiments prove that our PCPAU-Net outperforms other state-of-the-art methods.