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SUMMARY:Directional Framelets with Low Redundancy and Directional Quasi-ti
ght Framelets - Bin Han (University of Alberta\; University of Alberta)
DTSTART:20190219T114000Z
DTEND:20190219T121500Z
UID:TALK120019@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Edge singularities are ubiquitous and hold key
information
for many high-dimensional problems. Consequently\, directional
represen
tation systems are required to effectively capture edge singularities
f
or high-dimensional problems. However\, the increased angular resolution o
ften
significantly increases the redundancy rates of a directional syst
em. High
redundancy rates lead to expensive computational costs and lar
ge storage
requirement\, which hinder the usefulness of such directiona
l systems for
problems in moderately high dimensions such as video proc
essing. In this talk\,
we attack this problem by using directional tens
or product complex tight
framelets with mixed sampling factors. Such in
troduced directional system has
good directionality with a very low red
undancy rate $frac{3^d-1}{2^d-1}$\,
e.g.\, the redundancy rates are $2$
\, $2frac{2}{3}$\, $3frac{5}{7}$\,
$5frac{1}{3}$ and $7frac{25}{31}$ fo
r dimension $d=1\,ldots\,5$. Our numerical
experiments on image/video d
enoising and inpainting show that the performance
of our proposed direc
tional system with low redundancy rate is comparable or
better than sev
eral state-of-the-art methods which have much higher redundancy
rates.
In the second part\, we shall discuss our recent developments of
direct
ional quasi-tight framelets in high dimensions. This is a joint work with<
br>Chenzhe Diao\, Zhenpeng Zhao and Xiaosheng Zhuang.
LOCATION:Seminar Room 1\, Newton Institute
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