Unsupervised Range-Nullspace Learning Prior for Multispectral Images Reconstruction

Snapshot Spectral Imaging (SSI) techniques, with the ability to capture both spectral and spatial information in a single exposure, have been found useful in a wide range of applications. SSI systems generally operate within the 'encoding-decoding' framework, leveraging the synergism of optical hardware and reconstruction algorithms. Typically, reconstructing desired spectral images from SSI measurements is an ill-posed and challenging problem. Existing studies utilize either model-based or deep learning-based methods, but both have their drawbacks. Model-based algorithms suffer from high computational costs, while supervised learning-based methods rely on large paired training data. In this paper, we propose a novel Unsupervised range-Nullspace learning (UnNull) prior for spectral image reconstruction. UnNull explicitly models the data via subspace decomposition, offering enhanced interpretability and generalization ability. Specifically, UnNull considers that the spectral images can be decomposed into the range and null subspaces. The features projected onto the range subspace are mainly low-frequency information, while features in the nullspace represent high-frequency information. Comprehensive multispectral demosaicing and reconstruction experiments demonstrate the superior performance of our proposed algorithm.