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.

翻译：近年来，扩散概率模型在全色锐化领域逐渐受到关注并取得了最先进的性能。本文指出了直接应用扩散概率模型解决全色锐化这一逆问题时存在的缺陷：1) 直接从高斯噪声开始采样忽略了低分辨率多光谱图像作为先验信息；2) 低采样效率往往需要更多采样步骤。我们首先将全色锐化问题重新表述为逆问题的随机微分方程形式。在此基础上，我们提出了一种能同时解决上述两个问题的薛定谔桥匹配方法。我们针对所提出的薛定谔桥匹配方法设计了高效的深度神经网络架构。与已建立的基于深度学习的回归框架和最新的扩散概率模型框架相比，我们的方法在更少的采样步骤下实现了最先进的性能。此外，我们还讨论了薛定谔桥匹配与基于随机微分方程和常微分方程的其他方法之间的关系，以及其与最优传输的联系。代码将公开提供。