CODE-IF: A Convex/Deep Image Fusion Algorithm for Efficient Hyperspectral Super-resolution

Super-resolving remotely acquired hyperspectral images, often with low resolution (LR), is a critical signal processing technique, as it greatly affects the subsequent material classification and identification tasks. An economical approach in the remote sensing area is to fuse the spatial details extracted from the high-resolution (HR) counterpart multispectral image into the LR hyperspectral image, thereby inferring the desired HR hyperspectral image. Convex analysis has been shown to be an effective tool for the fusion mission, but it often relies on sophisticated regularization schemes to tackle this challenging inverse problem. In the existing literature, the deep plug-and-play strategy was proposed for fast implementation of those sophisticated regularizers, but just approximately without convergence guarantees. Thus, we introduce deep learning (in an alternative approach) to tailor a simple convex regularizer for efficient super-resolution. Remarkably, though typical deep fusion methods can tackle non-linear effect presented in real hyperspectral data, they often rely on big data and sophisticated network structures, which are often time-consuming and resource-intensive. Instead, our deep regularizer just needs a small-data-driven simple network architecture that implies better stability and tractability; we achieve so by reconsidering the role of deep learning as simply to guide the convex algorithm to search the fusion solution, rather than directly serving as the final solution. The proposed convex deep image fusion (CODE-IF) algorithm, with all the closed-form algorithmic expressions derived, achieves state-of-the-art hyperspectral super-resolution performance.