1. Wavelets Medical Image Processing Projects

2. 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 + TestWavelets/Medicine

3. ResearchResearch SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet Hospitalin Kristiansand / Arendal Mathematics - Computer Science - Medicine

4. Mathematics Computer Science Medicine SINTEF Unimed Ultrasound in Trondheim -Detection of blood vessel in ultra sound image The Norwegian Radiumhospital in Oslo -Linear accelerator -Computing patient position -Databases -Image processing ( Wavelets) Sørlandet Hospitalin Kristiansand -Bone thickness -Blood vessel thickness in liver Sørlandet Hospital in Arendal -IR diagnostic

5. Research The 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

6. DNR Linear Accelerator Databases Patient Position Image processing

7. Radiation Theraphy - Patient Position Referance pictureControl picture

8. Digital Image Processing Manipulation of images by computer Input ImageComputerOutput Image Digital Image Processing

9. Image Tranformation Original ImageTranformed Image

10. Histogram

11. Histogram Equalization

12. Convolution

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

14. Image Transformation Fourier Transformation (2-dim)

15. Wavelets New 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 …

16. Wavelet transform has been perhaps the most exciting development in the last decade to bring together researchers in several different fields: Seismic Geology Signal processing (frequency study, compression, …) Image processing (image compression, video compression,...) Denoising data Communications Computer science Mathematics Electrical Engineering Quantum Physics Magnetic resonance Musical tones Diagnostic of cancer Economics … Interesting applications The subject of Wavelets is expanding at a tremendous rate

17. Introduction to Wavelets

18. Wavelets are building blocks that can quickly decorrelate data. At the present day it is almost impossible to give a precise definition of wavelets. The research field is growing so fast and novel contributions are made at such a rate that even if one manages to give a definition today, it might be obsolute tomorrow. One, very vague, way of thinking about wavelets could be: Wavelets = Building blocks Wavelets are building blocks for general functions.Wavelets are building blocks for general functions. Wavelets have space-frequency localization. Wavelets have space-frequency localization. Wavelets have fast transform algorithms. Wavelets have fast transform algorithms.

19. Wavelets are mathematical functions that can cut up data into different frequency components, and then study each component with a resolution matched to its scale. Wavelets have advantages over traditional Fourier methods in analyzing physical situation where the signal is transient or contains discontinuities and sharp spikes. Frequency / Transient signals / Discontinuity Adopting a whole new mindset or perspective in prosessing data Data

20. Wavelets - Different scales

21. 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…).

22. Image Tranformation Details Original Image Details Image The rest of the Image

23. Discrete Wavelet-transformation

24. Compress 1:50 JPEGWavelet Original

25. Analysis /Synthesis Example J=5 Num of Samples: 2 J = 32

26. Analysis Synthesis J=5 Sampling: 2 5 = 32 j=4j=5j=3j=2j=1j=0

27. j=4j=5j=3j=2j=1j=0

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

29. Wavelet Transform Morlet Wavelet Fourier/Wavelet Fourier Wavelet

30. Wavelet Transform Morlet Wavelet Fourier/Wavelet Fourier Wavelet

31. Wavelet Transform Morlet Wavelet - Visible Oscillation

32. Wavelet Transform Morlet Wavelet - Non-visible Oscillation [1/2]

33. Wavelet Transform Morlet Wavelet - Non-visible Oscillation [2/2]

34. Wavelets Basic Knowledge - Informatics - Programming / Object oriented (Java / C++) - Mathematics - Lineær algebra(Vektor Space / Basis Functions / Matrices / … ) - Fourier Analysis - Statistics - Physics

35. Definition of The Continuous Wavelet Transform CWT The continuous-time wavelet transform (CWT) of f(x) with respect to a wavelet  (x): L 2 (R)

36. Wavelet Transform

37. Wavelet Transform Tumour

38. The Norwegian Radiumhospital Mammography Diameter Relative contrast Number of microcalcifications

39. The Norwegian Radiumhospital Mammography - Mexican Hat - 2 Dim

40. The Norwegian Radiumhospital Mammography

41. Arthritis Measure of bone Morlet External part E/I bone edge Krsand

42. Thickness of blood vessel in liver Morlet Krsand

43. ThicknessThickness Mexican Hat Krsand

44. Arendal Diagnostics - IR radiation

45. Ultrasound Image - Edge detection SINTEF – Unimed – Ultrasound - Trondheim -Ultrasound Images -Egde Detection -Noise Removal -Egde Sharpening -Edge Detection -Edge Computation

46. Ultrasound Image - Edge detection SINTEF – Unimed – Ultrasound - Trondheim Aorta with ProthesisUltra Sound Image

47. Edge Detection Convolution

48. Edge detection Wavelet Mexican Hat

49. Edge detection Scalogram

50. Edge detection One beam

51. Edge detection Scalogram

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

53. Edge detection Wavelet - Max Energy Scale

54. Edge detection Wavelet - Different Edges

55. Methods for prepreparing of Image in front of Wavelet transform 1Noise removal Hard Soft Semi-soft 2Egde sharpening 3Different Wavelets

56. Noise Removal Thresholding HardSoftSemi-Soft

57. Noise Removal Syntetic Image 45 Wavelets - 500.000 test Original Original+ point spread function + white gaussian noise

58. Noise Removal Syntetic Image

59. Noise Removal Ultrasound Image Original Semi-soft Soft

60. Edge sharpening

61. Different Wavlets

62. Edge Computing

63. Mathematical Image Operation - Application

65. End