L1范数和分裂Bregman的遥感影像变分融合模型

Remote sensing image variational fusion model based on L1 norm and split Bregman

目前,一些基于变分的Pan-sharpening方法是通过梯度下降法极小化能量泛函来实现融合,但梯度下降法在靠近极小值时收敛速度会减慢。若变分模型中包含有L1范数的不可微项时,梯度下降法存在鲁棒性不高、计算复杂的问题。该文根据L1范数能保持图像的几何纹理、分裂Bregman对含有L1范数的泛函收敛速度快的特点,在已有的变分模型基础上,将L1范数加入到模型中,构建能量泛函代价函数,并通过分裂Bregman迭代极小化能量泛函。在Worldview-2数据集上的融合结果表明,该方法可以生成同时具有高光谱和高空间分辨率的图像。

At present, some Pan-sharpening based on variational methods are fused by minimizing the energy functional by gradient descent algorithm, but the convergence rate of the gradient descent method decreases when it near the minimum. And if the variational model contains the no differentiable of L1 norm, the gradient descent method has the problems of low robustness and complex computation. In this paper, according to the characteris- tics of L1 norm can keep the geometric texture of the image, split Bregman iterative has a fast convergence speed to the functional which contains L1 norm, so on the basis of the existing variational model, the L1 norm is added to the model, the energy functional cost function is constructed, and through the split Bregman iterative minimal energy functional. The fusion results on the Worldview-2 shows that the method in this paper can generate images with high spectral and high spatial resolution simultaneously.