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Wavelets - Fagside fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htm

Hovedprojekt våren 2004 Bruk av Wavelets (en relativt ny matematisk metode) innen medisinsk bildebehandling. Wavelets - Fagside http://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htm.

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Wavelets - Fagside fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htm

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  1. Hovedprojekt våren 2004Bruk av Wavelets (en relativt ny matematisk metode)innen medisinsk bildebehandling

  2. Wavelets - Fagsidehttp://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htm

  3. Prosjekter våren 2004Matematisk behandling av medisinsk bilde-informasjonUbegrenset sett av oppgaver av alle vanskelighetsgrader (fra ingen matematikk til avansert matematikk) - Bruk av Wavelets til å bestemme brystkreftsvulster på tidlig stadium. Oppdragsgiver: Det Norske Radiumhospital i Oslo (DNR). - Bruk av Wavelets til å bestemme blodårekanter fra ultralydbilder. Oppdragsgiver: SINTEF Unimed Ultralyd i Trondheim. - Bruk av Wavelets til å bestemme benmasse i kroppen. Oppdragsgiver: Sørlandet Sykehus i Kristiansand. - Bruk av Wavelets til å bestemme blodåretykkelse i lever. Oppdragsgiver: Sørlandet Sykehus i Kristiansand. - Bruk av bl.a. Wavelets innen diagnostikk vha IR. Oppdragsgiver: Sørlandet Sykehus i Arendal.

  4. Tittel - Eksempel på oppgavedefinisjon DNR

  5. Internasjonalt samarbeid Resterende sider (på engelsk) er utarbeidet i forbindelse med en invitasjon jeg fikk til en internasjonal matematikk-konferanse i Baltikum høsten 2003 for å holde foredrag om mitt arbeid med bruk av Wavelets (en relativt ny matematisk metode) innen matematisk behandling av medisinsk bildeinformsjon.

  6. Introduction Per Henrik Hogstad Associate Professor Agder University College Faculty of Engineering and Science Dept of Computer Science Grooseveien 36, N-4876 Grimstad, Norway Telephone: +47 37253285 Email: Per.Hogstad@hia.no

  7. 1 3 2 4

  8. Introduction Per Henrik Hogstad - Mathematics - Statistics - Physics (Main subject: Theoretical Nuclear Physics) - Computer Science - Programming / Objectorienting - Algorithms and Datastructures - Databases - Digital Image Processing - Supervisor Master Thesis - Research - PHH : Mathem of Wavelets + Computer Application Wavelets/Medicine - Students : Application + Test Wavelets/Medicine

  9. Research Mathematics - Computer Science - Medicine SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet hospital in Kristiansand / Arendal

  10. Mathematical Image Operation - Application

  11. WaveletsNew mathematical method with many interesting applications Divide a function into parts with frequency and time/position information Signal Processing - Image Processing - Astronomy/Optics/Nuclear Physics Image/Speech recognition - Seismologi - Diff.equations/Discontinuity …

  12. Definition of The Continuous Wavelet Transform CWT The continuous-time wavelet transform (CWT) of f(x) with respect to a wavelet (x): L2(R)

  13. Fourier-transformation of a square wave f(x) square wave (T=2) N=1 N=2 N=10

  14. Fourier transformation

  15. Fourier transformation

  16. Fourier transformation

  17. Fourier transformation

  18. CWT - Time and frequency localization Time Frequency Small a: CWT resolve events closely spaced in time. Large a: CWT resolve events closely spaced in frequency. CWT provides better frequency resolution in the lower end of the frequency spectrum. Wavelet a natural tool in the analysis of signals in which rapidly varying high-frequency components are superimposed on slowly varying low-frequency components (seismic signals, music compositions, pictures…).

  19. Fourier - Wavelet  t  a=1/2 Signal Time Inf Fourier Freq Inf Wavelet Time Inf Freq Inf a=1 a=2 t

  20. Filtering / Compression Data compression Remove low W-values Highpass-filtering Lowpass-filtering Replace W-values by 0 for high a-values Replace W-values by 0 for low a-values

  21. Wavelet TransformMorlet WaveletFourier/Wavelet Fourier Wavelet

  22. Wavelet TransformMorlet WaveletFourier/Wavelet Fourier Wavelet

  23. Wavelet TransformMorlet Wavelet - Visible Oscillation

  24. Wavelet TransformMorlet Wavelet - Non-visible Oscillation [1/2]

  25. Wavelet TransformMorlet Wavelet - Non-visible Oscillation [2/2]

  26. Matcad ProgramWavelet Transform

  27. CWT - DWT CWT DWT Binary dilation Dyadic translation Dyadic Wavelets

  28. Analysis /SynthesisExample J=5 Num of Samples: 2J = 32

  29. AnalysisSynthesisJ=5 Sampling: 25 = 32 j=5 j=4 j=3 j=2 j=1 j=0

  30. Discrete Wavelet-transformation

  31. Original Compress 1:50 JPEG Wavelet

  32. ResearchThe Norwegian Radiumhospital in Oslo - Control of the Linear Accelerator - Databases (patient/employee/activity)- Computations of patientpositions- Mathematical computations of medical image information - Different imageformat (bmp, dicom, …) - Noise Removal - Graylevel manipulation (Histogram, …) - Convolution, Gradientcomputation - Multilayer images - Transformations (Fourier, Wavelet, …) - Mammography - ... Wavelet

  33. The Norwegian RadiumhospitalMammography Diameter Relative contrast Number of microcalcifications

  34. The Norwegian RadiumhospitalMammography - Mexican Hat - 2 Dim

  35. The Norwegian RadiumhospitalMammography

  36. Morlet ArthritisMeasure of bone External part External part E/I bone edge E/I bone edge

  37. Ultrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - Trondheim - Ultrasound Images- Egde Detection- Noise Removal- Egde Sharpening- Edge Detection

  38. Edge DetectionConvolution

  39. Edge detectionWavelet Mexican Hat

  40. Edge DetectionWavelet -Scale Energy Wavelet Transform Inv Wavelet Transform Wavelet scale dependent spectrum A measure of the distribution of energy of the signal f(x) as a function of scale. Energy of the signal

  41. Edge detectionWavelet - Max Energy Scale

  42. Edge detectionWavelet - Different Edges

  43. Noise RemovalThresholding Hard Soft Semi-Soft

  44. Noise RemovalSyntetic Image45 Wavelets - 500.000 test Original + point spread function + white gaussian noise Original

  45. Noise RemovalSyntetic Image

  46. Semi-soft Noise Removal Ultrasound Image Original Soft

  47. Edge sharpening

  48. Edge detection

  49. Edge detection Scalogram

  50. Edge detection Scalogram

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