Construction Of Shearlet Frames With Dilation Factor A

By scaling,shearing and translation affine transformations for the basis function,shearlet function with different characteristics are generated.Shearlet functions have the optimal approximation properties for the singular curve and curved surface of high dimensional signal,consequently it can better capture the information of image edge.In particular,Shearlet frame simultaneously has multi-resolution analysis,anisotropy,direction sensitivity,frequency division and the optimal approximation properties,so it is widely concerned by scholars and widely used in function generation,signal image processing.Therefore,carrying out the research on shearlet frame that not only has theoretical significance but also has important application value.The main contents:Firstly,for any positive integer scale factor a(a ? 2),we construct a class of piecewise smooth,symmetric,compactly supported auxiliary function,and discuss properties of this kind of auxiliary function,which provide security conditions for construction of good properties of paseval shearlet frame based on the auxiliary function.Secondly,using the pseudo polar expression,variable substitution,frequency domain segmentation tools and methods,the construction methods of paseval shearlet frame with dilation factor a is given in two-dimensional and three-dimensional space,this paseval shearlet frame is generated by a single variable function.If the given the function is infinitely differentiable,compactly supported,band-limited,the constructed paseval shearlet frame with dilation factor a is also infinitely differentiable,compactly supported.