一类shearlet框架函数的构造

Construction of a type of shearlet frame function

由于经典小波在处理高维问题中得不到很好的结果,所以近些年人们提出了多种非经典小波来克服经典小波的不足.shearlet便属于非经典小波之一,它具有多方面的优越性,但不具有经典小波那样的正交性.为了使不具有正交性的函数列完成重构任务,框架理论在shearlet理论中得到了系统的应用,即用框架来代替正交基完成重构任务.采用先在频域划分再利用傅里叶逆变换转换到时域的重构图像的思路,在推导出shearlet框架构造方法的基础上,给出了三角函数类型的shearlet框架函数.

Good results can＇t be obtained for high dimensional problems by classic wavelets since the sensitivity of direction is not good. To overcome this deficiency, nonclassical wavelets, such as the shearlet, have been proposed in recent years. The shearlet has many advantages, but it is not orthogonal while the classic wavelet is. In order to complete reconstruction using the sequence of functions without orthogonality, frame theory has been applied in shearlet theory comprehensively to replace orthogonal basis with frame. In this paper, the shearlet framework is derived with structure method, and a concrete shearlet frame function is put forward.