GIANCourseon
TheoryandApplicationofWaveletsandFramelets
28December2017–04January2018
Overview
As the major tool for multiscale data analysis, wavelets have a wide scope of applications in mathematics,engineering,physics,sciences,andindustries.Forexample,waveletshavebeenadoptedinJPEG-2000standardforimage compression, and wavelet subdivision algorithms have been used in animation movie industry. Being amultidisciplinary researcharea,waveletsand frameletsareveryeffective for representingvarious functionsanddata.Thegreatsuccessofwaveletsandframeletslargelyliesintheirmanydesiredpropertiessuchasmultiscalestructure, sparse representation, efficient approximation schemes, good time-frequency localization, and fastcomputational algorithms. In comparison to traditional wavelets, framelets have the desired properties ofredundancyforrobustnessandflexibilityforadaptivecustomdesign.Thecurrentdevelopmentsonwavelettheoryarefocusingonframeletaspectsandtheirapplicationsinhigh-dimensionaldataanalysis.Forexample,algorithmsusing framelets currently provide the-state-of-the-art results in image processing, and are popular in geometricmodellingprocessing.
Objectives
Introducethealgorithmsandbasictheoryofwaveletsandframeletstostudentsandinterestedresearchers.Thiswillequipthestudentsandresearchersthebasicknowledgeonwavelettheory,teachthemhowtodevelopandimplement their own fast framelet/wavelet transforms, and introduce them to design their own wavelets andframelets for their own purposes. Bring the students and researchers to thewide scope of applications usingwaveletsandframelets.Therearenumerousapplicationsofwaveletsandframeletsandwemainlyconcentrateontheirapplicationstosignal/imageprocessingandgeometricmodelling.Throughoutthelecturesandtutorials,thestudentsandresearcherswillbecomefamiliarwithhowtoconcretelyuse/implementwaveletsandframeletstosolve some practical problems in applications. Present some most recent developments on wavelets andframelets. Thisallows the studentsand researchers tobecomeawarewhatare thecurrent frontiersofwavelettheoryandwhatarethepossiblefurtherdevelopmentsandapplicationsofwaveletsandframelets.Thestudents'knowledgeabout the course contentwill be raised to the level such that theywill beable tousewavelets andframeletsfortheirownapplicationsandresearch.
Modules A: Fast Framelets and Wavelet Transforms
TopicsofLecture:• Ashortnaïveintroductiontowaveletsforeveryone:Whatisawavelet?• Perfect reconstruction, sparsityandvanishingmomentsof frameletand
wavelettransforms• Multilevelstructureofframelet/wavelettransformsandtheirvariants• How to implement fast framelet and wavelet transforms for practical
data• Howtoprocesswaveletorframeletcoefficients:waveletshrinkage
TopicsofTutorial:• Introductiontoframeletandwavelettransforms• Demonstration and examples on wavelet transforms using matlab
toolbox• Exploreframelettransformsanddiscusstheirdifferencestowavelets• Waveletapplicationstothesignaldenoisingproblem
Modules B: Mathematical Theory of Wavelets and Framelets
TopicsofLecture:• Framesandbases inHilbert spaces, in finitedimensional spaces, and in
shift-invariantspaces• Samplingtheoremsinshift-invariantspacesforsignalprocessing• Multiresolutionanalysisandorthogonalwavelets• CompactlysupportedDaubechiesorthogonalwavelets• Refinablefunctionsandtheoryoftightframelets• Basicdesirablepropertiesofwaveletsandframelets
TopicsofTutorial:• Explore sampling theorems in shift-invariant spaces generated by B-
splines• Designandimplementorthogonalwavelets• Howtodesignandimplementtightframeletfilterbanks• Use subdivision schemes and cascade algorithms to plot wavelets and
refinablefunctions
Modules C: Applications of Wavelets and Framelets
TopicsofLecture:• Tensorproductionandhigh-dimensionalwaveletsandframelets• Introductionofsubdivisionschemesandcascadealgorithms• Waveletsubdivisionforcomputergraphicsandgeometricmodeling• Dual-tree complex wavelet transform and directional complex tight
frameletsTopicsofTutorial:
• Exploretensorproductwavelet/frameletalgorithmsforhigh-dimensionaldata
• Imagemodelsandwavelet-basedalgorithmsforimageprocessing• Usesubdivisionschemestogeneratesubdivisioncurvesforgeometric
modeling• Applicationsofdirectionalframeletsandwaveletstoimageprocessing• Problemsolvingsessionwithexamplesinimageprocessing
You Should Attend If…
• You are students at all levels (BTech/MSc/MTech/PhD/Post Doc) orFacultyfromreputedacademicinstitutionsandtechnicalinstitutions.
• You are executives, engineers and researchers from manufacturing,serviceandgovernmentorganizationsincludingR&Dlaboratories.
Max. No. of Participants
50
Fees
Participantsfromabroad:US$200MSc/M.Phil/B.Tech/M.Tech.Students:Rs.500/-Ph.D.Student/PostDoctoralParticipants:Rs.1,000/-FacultyParticipants:Rs.1,000/-GovernmentResearchOrganizationParticipants:Rs.3,000/-IndustryParticipants:Rs.3,000/-Theabovefeeincludeslunch,instructionalmaterials,24hoursinternetfacility.
Accommodation
The participants may be provided with hostel accommodation, depending onavailability,onpaymentbasis.
Foranyquery,[email protected].
TheFaculty
Prof. Bin Han is a full professor ofmathematics at the Department ofMathematicalandStatisticalSciencesin the University of Alberta, Canada.TheresearchareaofBinHanincludesapplied harmonic analysis, wavelet
analysis and their applications in computer graphics,image/signal processing, and numerical algorithms. BinHan serves as an editor for four academic SCI journalsincluding Applied and Computational Harmonic Analysisand Journal of Approximation Theory. Bin Han is anauthor of more than 85 papers in top academic SCIjournals and is the author of the book: Framelets andwavelets: algorithms, analysis, and applications.According to SCI citation for recent 10-year work, he isrankedwithintop200inmathematicswithseveralofhispaperscited299,132and118times.Hehasbeeninvitedtopresentmany invited talks including fiveplenary talksin major international conferences in the area ofwavelets, approximation theory, and applied andcomputational harmonic analysis. For example, hepresenteda1-hourplenarytalk inthe13th InternationalConference on Approximation Theory in March 2010 atSan Antonio, USA. He served as the director of theAppliedMathematicsInstituteattheUniversityofAlbertafrom2012to2015.Hehassupervised5PhDstudents,4MSc students, and 5 postdoctoral fellows. For moredetails,pleasevisithttps://sites.ualberta.ca/~bhan/.
Dr. Niraj K. Shukla is working as anAssistant Professor in Discipline ofMathematics, IIT Indore.His researchinterest is Wavelet, Frame andHarmonicAnalysis.
Formoredetails,pleasevisithttp://iiti.ac.in/people/~nirajshukla/.
Duration:
December28,2017-January04,2018
CourseCo-ordinatorDr. Niraj Kumar Shukla Assistant Professor Discipline of Mathematics IIT Indore, Khandwa Road, Simrol Indore- 453 552, Madhya Pradesh Tel: +91 732 4306 506 +91 731 2438 947 Email: [email protected] http://iiti.ac.in/people/~nirajshukla/ ............................................................. Course Web-page: http://iiti.ac.in/people/~nirajshukla/Gian Registration Link: http://gian.iiti.ac.in/register.php
