Frames and Spline Framelets

Frames can be seen as a generalization of orthonormal bases, which not only maintain useful characteristics of orthonormal bases but also allow more flexibility in applications. The applications of frames include communication and image processing, as its characteristic inherited from orthonormal bases helps speed up the transmitting and processing time while its additional flexibility adds to frames the ability to reconstruct lost information. In this project, we study the construction of a class of tight frames in Euclidean spaces. Also, we use Fourier transforms and the techniques of Multi-Resolution Analysis (MRA) in wavelet analysis to investigate a class of tight spline framelets