master thesis 2005 wavelets (a relative new mathematical method) in medical image processing
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Master Thesis 2005 Wavelets (A relative new Mathematical method) in Medical Image Processing. Wavelets http://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htm. Interesting applications The subject of Wavelets is expanding at a tremendous rate. - PowerPoint PPT PresentationTRANSCRIPT
Master Thesis 2005Master Thesis 2005WaveletsWavelets (A relative new Mathematical method) (A relative new Mathematical method)in in Medical Image ProcessingMedical Image Processing
Master Thesis 2005Master Thesis 2005WaveletsWavelets (A relative new Mathematical method) (A relative new Mathematical method)in in Medical Image ProcessingMedical Image Processing
WaveletsWaveletshttp://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htmhttp://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htmWaveletsWaveletshttp://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htmhttp://fag.grm.hia.no/fagstoff/perhh/htm/fag/matem/datwwww/wavelet.htm
•• Wavelet transform has been perhaps the most exciting development in the last decade to bring together researchers in several different fields:
Seismic GeologySignal processing (frequency study, compression, …)Image processing (image compression, video compression, ...)Denoising dataCommunicationsComputer scienceComputer scienceMathematicsMathematicsElectrical EngineeringQuantum PhysicsMagnetic resonanceMusical tonesDiagnostic of cancerEconomics…
Interesting applicationsInteresting applicationsThe subject of Wavelets is expanding at a tremendous rateThe subject of Wavelets is expanding at a tremendous rateInteresting applicationsInteresting applicationsThe subject of Wavelets is expanding at a tremendous rateThe subject of Wavelets is expanding at a tremendous rate
Medical co-operationMedical co-operationThe Norwegian Radiumhospital in OsloThe Norwegian Radiumhospital in OsloMedical co-operationMedical co-operationThe Norwegian Radiumhospital in OsloThe 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
Co-operationCo-operationCo-operationCo-operation
SINTEF Unimed Ultrasound in Trondheim
The Norwegian Radiumhospital in Oslo
Sørlandet hospital in Kristiansand / Arendal
Mathematics - Computer Science - Medicine
International Co-operationInternational Co-operation
After an invitation to a mathematical conferencein Balticum 2003, I have had lessons in different countriesand the international co-operation now includes Norway, Sweden, Scotland, Germany, Estonia and Russia
Definition of The Continuous Wavelet Transform Definition of The Continuous Wavelet Transform CWTCWTDefinition of The Continuous Wavelet Transform Definition of The Continuous Wavelet Transform CWTCWT
dxxfxfbafWbaW baba )()(),]([),( ,,
0 , )(, 2 aRbaRLf
The continuous-time wavelet transform (CWT)of f(x) with respect to a wavelet (x):
][ fW),]([ bafW
)(xf
)(xL2(R)
a
bxaxba
2/1, || )(
dadbxbaWaC
xf ba )(),(11
)( ,2
)(0,1 x )(0,2 x )(1,2 x
CWTCWT - DWT - DWTCWTCWT - DWT - DWT
dxxfxfbafWbaW baba )()(),]([),( ,,
dadbxbaWaC
xf ba )(),(11
)( ,2
CdC 0
)(2
a
bxaxba 2/1
, || )(
CWT
DWT
m
m
anbb
aa
00
0
nxx mmnm 22 )( 2/
,
m
m
nb
a
2
2
1 2 00 ba
Binary dilationDyadic translation
Dyadic Wavelets
voicea called group, one as processed are of pieces v
octaveper voicesofnumber 2
nm,
/10
va v
Fourier transformationFourier transformation
Wavelet TransformWavelet TransformMorlet Wavelet - Non-visible OscillationMorlet Wavelet - Non-visible OscillationWavelet TransformWavelet TransformMorlet Wavelet - Non-visible OscillationMorlet Wavelet - Non-visible Oscillation
][fWa
11ψ2
][fWa
12ψ2
xex x
2ln
2cos)(
2
210)0.01(x1 1000e(x)f
9,11 xif x)5sin(2)(
11,,9 xif (x)(x)f
1
12 xf
f
(x)f1
(x)f2
Scalogram
Scalogram
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets: Detecting Breath Cancer at an early stage
The Norwegian Radiumhospital in Oslo (DNR)
brPbrT
a
T
y
brPbr
2
1
a2π
1b,a
e2)r(Ψx
Mammography Wavelet transformed
Definition DNRDefinition DNR
The Norwegian Radiumhospital in Oslo (DNR)
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets: Detecting Blood Vessel in Ultra Sound Image
SINTEF Unimed Ultralyd in Trondheim
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets: Compute Bone Thickness
Sørlandet hospital in Kristiansand
[f]Wa
1ψ2
-Wavelets:Compute Blood Vessel Thickness in LiverSchistosomiasis
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets: IR Diagnostics
Sørlandet hospital in Arendal
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets: Video Compression
HiA – German Company
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
-Wavelet Program system in Mathematica, Mathlab, Mathcad, JavaDifferent WaveletsModulus and Phase Representation in Complex Wavelets
HiA
][fWa
12ψ2
Scalogram
Different advanced analyse tools.Prepare different suitable program system.Special study of phase representation.
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Continuous Wavelet TranformECG Recognition Based on Phase and Modulus Representationand Hidden Markov Models
Sørlandet Hospital
Wavelet transforms have been applied (CWT/DWT) to ECG for - ehancing late potentials- reducing noise- QRS detection- normal and abnormal beat recognition
CWT of complex waveletsPhase representation study of local symmetry / asymmetry
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Statistical Analysis of Image Differences by Wavelet Decomposition
Sørlandet Hospital
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
Sørlandet Hospital
- Application of Wavelet Transforms to Blood Flow VelocimetryGeneral: Velocity in Fluid / Gas
Ultrasound high fractional bandwidth and large time-bandwidth signalsDoppler Effect Wideband / Wavelet Transform
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
Sørlandet Hospital
- Wavelets Transform for speaker identification
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets to Suppress Noise in Biomedical Images
Sørlandet Hospital
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets Technicques for Encoding Magnetic Resonance Images
Sørlandet Hospital
Master Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in MedicineMaster Thesis 2005Master Thesis 2005Mathematical Image Processing in MedicineMathematical Image Processing in Medicine
- Wavelets Technicques for Detecting Pipe Connection in Video Image
Sence Technology
MatMathhcad Programcad ProgramWavelet TransformWavelet TransformMatMathhcad Programcad ProgramWavelet TransformWavelet Transform
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