information for many high-dimensional problems. Co nsequently\, directional

representation systems are required to effectively capture edge singular ities

for high-dimensional problems. However\, the increased angular resolution often

signific antly increases the redundancy rates of a directio nal system. High

redundancy rates lead to expen sive computational costs and large storage

requ irement\, which hinder the usefulness of such dire ctional systems for

problems in moderately high dimensions such as video processing. In this talk \,

we attack this problem by using directional tensor product complex tight

framelets with mix ed sampling factors. Such introduced directional s ystem has

good directionality with a very low r edundancy rate $frac{3^d-1}{2^d-1}$\,

e.g.\, th e redundancy rates are $2$\, $2frac{2}{3}$\, $3fra c{5}{7}$\,

$5frac{1}{3}$ and $7frac{25}{31}$ fo r dimension $d=1\,ldots\,5$. Our numerical

expe riments on image/video denoising and inpainting sh ow that the performance

of our proposed directi onal system with low redundancy rate is comparable or

better than several state-of-the-art method s which have much higher redundancy

rates. In t he second part\, we shall discuss our recent devel opments of

directional quasi-tight framelets in high dimensions. This is a joint work with

Che nzhe Diao\, Zhenpeng Zhao and Xiaosheng Zhuang. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR