Shearlet变换与图像处理应用

Shearlet transform and its applications in image processing

Shearlet是一种新的多维函数稀疏表示工具,采用具有合成膨胀的仿射系统来构造基函数,具有数学结构简单、多分辨率、多方向性和局部化等优良特性,能够高效地捕获到多维数据的几何结构,更加适合处理图像等高维信号.在分析Shearlet变换的数学框架及其数字实现方法的基础上,介绍了它在图像处理中的部分应用,并对其研究前景进行了展望.

Shearlet, a new sparse representation tool of multidimensional function, is based on affine systems with composite dilations. It not only provides a simple mathematical framework, multi-resolution, multi-direction and local representation, but is also more efficient in capturing the geometry of multidimensional data and more suitable for image processing. This paper introduces mathematical framework of the shearlet and its digital implementation. Then several applications are surveyed. Finally, some further work on shearlet is also presented.