Framelet lifting in image processing
Dayong Lu, Tie-yong Feng · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2010
To obtain appropriate framelets in image processing, we often need to lift existing framelets. For this purpose the paper presents some methods which allow us to modify existing framelets or filters to construct new ones. The relationships of matrices and their eigenvalues which be used in lifting schemes show that the frame bounds of the lifted wavelet frames are optimal. Moreover, the examples given in Section 4 indicate that the lifted framelets can play the roles of some operators such as the weighted average operator, the Sobel operator and the Laplacian operator, which operators are often used in edge detection and motion estimation applications.