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題目：Fast?Image?Denoising?and?Alignment?Via?Steerable?Transforms
時(shí)間：2025年8月14日 14:00-15:00
地點(diǎn)：機(jī)械與動(dòng)力工程學(xué)院 F310會(huì)議室
邀請(qǐng)人：劉思羽 副教授
Biography
Dr.?Yunpeng?Shi?is?an?assistant?professor?in?the?Department?of?Mathematics?at?the?University?of?California,?Davis,?where?he?has?been?since?the?fall?of?2023.?Prior?to?joining?UC?Davis,?he?was?a?postdoctoral?research?associate?in?the?Program?in?Applied?and?Computational?Mathematics?at?Princeton?University,?working?under?the?supervision?of?Professor?Amit?Singer?from?2020?to?2023.?He?earned?her?Ph.D.?in?Mathematics?from?the?University?of?Minnesota,?where?he?was?supervised?by?Professor?Gilad?Lerman.
Dr.?Shi’s?research?lies?at?the?intersection?of?mathematics,?computation,?and?data?science.?His?work?spans?3D?computer?vision?and?image?processing,?cryo-electron?microscopy?imaging?for?protein?molecules,?robust?estimation?and?outlier?detection,?scalable?computational?methods,?nonlinear?dimension?reduction?and?manifold?learning,?and?optimal?transport.
Abstract
In?this?talk,?Dr.?Shi?explore?two?classical?image?processing?tasks?motivated?by?cryo-electron?microscopy?imaging:?tomographic?image?denoising?and?rigid?image?registration.?Both?tasks?inherently?involve?operations?of?2D?rotations,?where?leveraging?specific?transforms?can?significantly?enhance?the?speed?and?robustness?of?the?algorithms.?
In?the?first?part?of?the?talk,?Dr.?Shi?will?introduce?an?unsupervised?image?denoiser?based?on?estimating?the?covariance?matrix?of?clean?images.?A?key?insight?is?that?if?the?image?manifold?is?invariant?under?global?in-plane?rotations,?this?symmetry?can?be?exploited?to?accelerate?computations?and?reduce?dimensionality.?Dr.?Shi?will?discuss?recent?advances?in?fast?expansion?into?steerable?bases?that?allow?us?to?efficiently?utilize?this?rotational?symmetry,?leading?to?a?thousandfold?improvement?in?the?speed?of?covariance?estimation?over?existing?methods.?This?technique?has?been?successfully?applied?to?joint?deconvolution?and?denoising?of?large-scale,?real-world?cryo-EM?images.?
In?the?second?part,?Dr.?Shi?will?present?a?fast?algorithm?for?aligning?images?using?optimal?transport.?Our?method?leverages?the?sliced?Wasserstein?distance?by?computing?the?1D?Wasserstein?distance?between?radial?line?projections?of?input?images.?By?applying?a?special?transform?to?the?frequency?domain,?Dr.?Shi?achieve?efficient?alignment?of?two?L?by?L?images?in?O(L^2?log?L)?operations?--?matching?the?complexity?of?alignment?using?Euclidean?distance.?I?will?demonstrate?the?robustness?of?our?method?to?translations?and?deformations.
Finally,?Dr.?Shi?will?comment?on?the?practical?limitations?of?both?methods?and?discuss?open?questions?that?remain,?highlighting?areas?for?future?exploration.
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ENGLISH
地址：上海市東川路800號(hào)上海交通大學(xué)閔行校區(qū)機(jī)械與動(dòng)力工程學(xué)院
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