Wavelets Medical Image Processing Projects Per Henrik Hogstad

Wavelets Medical Image Processing Projects

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

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 Hospital in Kristiansand - Bone thickness - Blood vessel thickness in liver Sørlandet Hospital in Arendal - IR diagnostic

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

DNR Linear Accelerator Databases Patient Position Image processing

Radiation Theraphy - Patient Position Referance picture Control picture

Digital Image Processing Manipulation of images by computer Input Image Computer Digital Image Processing Output Image

Image Tranformation Original Image Tranformed Image

Histogram

Histogram Equalization

Convolution

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

Image Transformation Fourier Transformation (2 -dim)

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

Interesting applications The subject of Wavelets is expanding at a tremendous rate • 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 …

Introduction to Wavelets

Wavelets = Building blocks 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 are building blocks that can quickly decorrelate data. • Wavelets are building blocks for general functions. • Wavelets have space-frequency localization. • Wavelets have fast transform algorithms.

Frequency / Transient signals / Discontinuity Adopting a whole new mindset or perspective in prosessing data Data • 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.

Wavelets - Different scales

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…).

Image Tranformation Details Image Original Image The rest of the Image

Discrete Wavelet-transformation

Original Compress 1: 50 JPEG Wavelet

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

Analysis Synthesis J=5 Sampling: 25 = 32 j=5 j=4 j=3 j=2 j=1 j=0

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]

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

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)

Wavelet Transform

Wavelet Transform Tumour

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 Krsand External part E/I bone edge

Thickness of blood vessel in liver Krsand Morlet

Krsand Thickness Mexican Hat

Arendal Diagnostics - IR radiation

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

Ultrasound Image - Edge detection SINTEF – Unimed – Ultrasound - Trondheim Ultra Sound Image Aorta with Prothesis

Edge Detection Convolution

Edge detection Wavelet Mexican Hat

Edge detection Scalogram

Edge detection One beam

Edge detection Scalogram

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

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

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

Different Wavlets

Edge Computing

Mathematical Image Operation - Application

Mathematical Image Operation - Application

End