基于求解Sylvester方程的多波段图像快速融合
Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation
摘要：
提出了一种快速多波段图像融合算法，将高空间分辨率的低光谱分辨率图像与低空间分辨率的高光谱分辨率图像进行融合。被公认的前向模型进行了探索，以形成观测的似然度。最大化的可能性导致解决西尔维斯特方程。通过利用与融合问题相关联的循环矩阵和下采样矩阵的性质，显式地获得了对应的Sylvester方程的封闭形式的解，摆脱了任何迭代更新步骤。再加上交替方向的乘法器和块坐标下降法，该算法可以很容易地推广到融合问题的先验信息，允许贝叶斯估计。仿真结果表明，该算法在与现有算法性能相当的基础上，显著降低了现有算法的计算复杂性。
英文摘要：
This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.
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