Neural Shrödinger Bridge Matching for Pansharpening
Zihan Cao Xiao Wu Liang-Jian Deng
Recent diffusion probabilistic models (DPM) in the field of pansharpening
have been gradually gaining attention and have achieved state-of-the-art (SOTA)
performance. In this paper, we identify shortcomings in directly applying DPMs
to the task of pansharpening as an inverse problem: 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. We first reformulate pansharpening into the
stochastic differential equation (SDE) form of an inverse problem. Building
upon this, we propose a Schr\"odinger bridge matching method that addresses
both issues.
  We design an efficient deep neural network architecture tailored for the
proposed SB matching.
  In comparison to the well-established DL-regressive-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.
  Code will be available.