TwP: Two-stage projection framework with manifold constraint for image reconstruction

Abstract

As an extensively studied task in computer vision, image reconstruction aims to reconstruct original data from acquired measurements. It is a highly ill-posedness inverse problem since a countably infinite number of feasible solutions exist. To achieve high-quality reconstruction performance, we propose a two-stage projection (TwP) framework built upon the projection technique and manifold constraint. We first exploit the generalized non-convex alternating projection method for image reconstruction in the pre-reconstruction stage, that incorporates the image manifold constraint implicitly imposed by deep denoiser. It provides a unified method to solve linear/non-linear inverse problems in a plug-and-play manner and deliver a good estimation. In the post-processing stage, a feed-forward network fine-tuned for a specific task is utilized to reproject the pre-reconstruction results onto the low-dimensional image manifold, which enables the outcomes to be in or closest to the manifold. Extensive experiments across various image reconstruction tasks, such as single-photon imaging, image compressive sensing, and image deblurring, demonstrate that the proposed TwP delivers promising results against some existing state-of-the-art algorithms in terms of objective and visual perceptions.