Neural Shrödinger bridge matching for pansharpening

Recent diffusion probabilistic models (DPMs) in the field of pansharpening have gradually gained attention and achieved state-of-the-art (SOT A) performance. In this paper, we identify shortcomings in directly applying DPMs to the task of pansharpening as an inverse problem, including 1) initiating sampling directly from Gaussian noise neglects the low-resolution multispectral image (LRMS) as a prior; 2) low sampling efficiency often necessitates a higher number of sampling steps. To address these shortcomings, we first reformulate pansharpening into the stochastic differential equation (SDE) form of an inverse problem. Building upon this, we propose a Schrodinger bridge (SB) matching method that addresses both issues. Moreover, we design an efficient deep neural network architecture tailored for the proposed SB matching. In comparison to the well-established deep learning (DL)-regression-based framework and the recent DPM framework, our method demonstrates SOTA performance with fewer sampling steps. Moreover, we discuss the relationship between SB matching and other methods based on SDEs and ordinary differential equations (ODEs), as well as its connection with optimal transport (OT). The code will be available at https: //github.com/294coder/PansharpeningShrodingerBridge.