Hovedprojekt vren 2004 Bruk av Wavelets en relativt
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
Prosjekter våren 2004 Matematisk behandling av medisinsk bilde-informasjon Ubegrenset 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.
Tittel - Eksempel på oppgavedefinisjon DNR
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.
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
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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
Research Mathematics - Computer Science - Medicine SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet hospital in Kristiansand / Arendal
Mathematical Image Operation - Application
Wavelets New mathematical method with many interesting applications Divide a function into parts with frequency and time/position information Signal Processing Image/Speech recognition … - Image Processing - Astronomy/Optics/Nuclear Physics - Seismologi - Diff. equations/Discontinuity
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)
Fourier-transformation of a square wave f(x) square wave (T=2) N=1 N=2 N=10
Fourier transformation
Fourier transformation
Fourier transformation
Fourier transformation
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…).
Fourier - Wavelet t Signal Fourier Wavelet Time Inf Freq Inf a=1/2 a=1 a=2 t
Filtering / Compression Data compression Remove low W-values Lowpass-filtering Highpass-filtering Replace W-values by 0 for low a-values Replace W-values by 0 for high a-values
Wavelet Transform Morlet Wavelet Fourier/Wavelet Fourier Wavelet
Wavelet Transform Morlet Wavelet Fourier/Wavelet Fourier Wavelet
Wavelet Transform Morlet Wavelet - Visible Oscillation
Wavelet Transform Morlet Wavelet - Non-visible Oscillation [1/2]
Wavelet Transform Morlet Wavelet - Non-visible Oscillation [2/2]
Matcad Program Wavelet Transform
CWT - DWT CWT DWT Binary dilation Dyadic translation Dyadic Wavelets
Analysis /Synthesis Example J=5 Num of Samples: 2 J = 32
Analysis Synthesis J=5 Sampling: 25 = 32 j=5 j=4 j=3 j=2 j=1 j=0
Discrete Wavelet-transformation
Original Compress 1: 50 JPEG Wavelet
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
The Norwegian Radiumhospital Mammography Diameter Relative contrast Number of microcalcifications
The Norwegian Radiumhospital Mammography - Mexican Hat - 2 Dim
The Norwegian Radiumhospital Mammography
Morlet Arthritis Measure of bone External part E/I bone edge
Ultrasound Image - Edge detection SINTEF – Unimed – Ultrasound - Trondheim - Ultrasound Images - Egde Detection - Noise Removal - Egde Sharpening - Edge Detection
Edge Detection Convolution
Edge detection Wavelet Mexican Hat
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.
Edge detection Wavelet - Max Energy Scale
Edge detection Wavelet - Different Edges
Noise Removal Thresholding Hard Soft Semi-Soft
Noise Removal Syntetic Image 45 Wavelets - 500. 000 test Original + point spread function + white gaussian noise Original
Noise Removal Syntetic Image
Semi-soft Noise Removal Ultrasound Image Original Soft
Edge sharpening
Edge detection
Edge detection Scalogram
Edge detection Scalogram
Edge detection
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