time-frequency analysis and wavelet transform oral presentation

Time-Frequency Analysis and Wavelet Transform Oral

PresentationAdvisor: 丁建均 and All Class Members

Student: 李境嚴ID: D00945001

What’s Today?

3

(1) Finding Instantaneous Frequency (2) Signal Decomposition(3) Filter Design (4) Sampling Theory (5) Modulation and Multiplexing (6) Electromagnetic Wave Propagation(7) Optics(8) Radar System Analysis (9) Random Process Analysis (10) Music Signal Analysis

(11) Acoustics (12) Biomedical Engineering (13) Spread Spectrum Analysis (14) System Modeling(15) Image Processing(16) Economic Data Analysis (17) Signal Representation (18) Data Compression (19) Seismology(20) Geology

XIII. Applications of Time–Frequency Analysis

Biomedical Engineering

Image Processing

Wavelet TransformKernel (Windows)

Laws Texture

Study of Classification of Lung Tumor Based on CT/PET Images Technique of studying image ( gray level) Training skill of machine learning

What’s Today?

Gray level studying DSP, Kernel( window)

Resolution of image 4000*3000, 1024*768, 640*480, 320*240

How about in Biomedical Image?

Why Image Processing?

The Biomedical Image TodayCT:

512*512PET:

128*128



Brain v.s. Lung Tumors

Introduction and Back ground Technique Experiments Discussion and Conclusion

Outline


Introduction

Lung Tumor High Death Ratio Nerve-less

Introduction

Introduction

Image Load

Pre-processin

g

Co-Registratio

n

ROIFeature Extraction

Classification

Co-Registrat

ion

Feature Extracti

on

Down / Up sampling ; Wavelet Transform

Wavelet ; Laws Texture ; Other Methods

Wavelet Transform:

Introduction--Wavelet Transform

J. J. Ding, 09 月 15 日上課資料 , P 43


Ivan W. Selesnick, Wavelet Transforms, 2007

Introduction


(2 ) ( ) ( )y n c n d n (2 1) ( ) ( )y n c n d n


Ivan W. Selesnick, W

avelet Transforms, 2007

Wavelet Transform: Improvement???

Haar !!


Haar Transform:



Wavelet Transform Haar Transform

Wavelet Transform:


J. J. Ding, 09 月 15 日上課資料 , P 46

Laws features The texture energy measures developed

by Kenneth Ivan Laws at the University of Southern California have been used for many diverse applications. These measures are computed by first applying small convolution kernels to a digital image, and then performing a nonlinear windowing operation.

Introduction—Laws Texture

http://www.ccs3.lanl.gov/~kelly/ZTRANSITION/notebook/laws.shtml

Laws features 3 element kernel 5 element kernel High order kernel


M.T. Suzuki, Y. Yaginuma, H. Kodama, A Texture Energy Measurement Technique for 3D Volumetric Data, 2009 IEEE International Conference on Systemshttp://www.ccs3.lanl.gov/~kelly/ZTRANSITION/notebook/laws.shtml

Laws features 3 element kernel

Level: [1 2 1];Edge: [-1 0 1];Spot: [-1 2 -1];



Laws features


Laws features 5 element kernel

L5 = [1, 4, 6, 4, 1]; E5 = [−1,−2, 0, 2, 1]; S5 = [−1, 0, 2, 0,−1]; R5 = [1,−4, 6,−4, 1]; % ripple W5 = [−1, 2, 0,−2, 1]; % wave



Laws features


Laws features Image processing --- 2D case

L5L5 L5E5 L5S5 L5R5 L5W5E5L5 E5E5 E5S5 E5R5 E5W5S5L5 S5E5 S5S5 S5R5 S5W5R5L5 R5E5 R5S5 R5R5 R5W5W5L5 W5E5 W5S5 W5R5 W5W5



Laws features



L5L5

E5E5

S5S5

R5R5

W5W5

CT - computed tomography PET - Positron emission

tomography

Introduction-- Background

CT - Computed Tomography Digital geometry processing is used to

generate a three-dimensional image of the inside of an object from a large series of two-dimensional X-ray images taken around a single axis of rotation .

http://translate.google.com/translate?hl=zh-TW&langpair=en|zh-TW&u=http://en.wikipedia.org/wiki/X-ray_computed_tomography


PET - Positron Emission Tomography A nuclear medicine imaging technique that produces a three-dimensional image or

picture of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule. Three-dimensional images of tracer concentration within the body are then constructed by computer analysis. In modern scanners, three dimensional imaging is often accomplished with the aid of a CT X-ray scan performed on the patient during the same session, in the same machine.

If the biologically active molecule chosen for PET is FDG, an analogue of glucose, the concentrations of tracer imaged then give tissue metabolic activity, in terms of regional glucose uptake. Although use of this tracer results in the most common type of PET scan, other tracer molecules are used in PET to image the tissue concentration of many other types of


http://en.wikipedia.org/wiki/Positron_Emission_Tomography

PET - Positron emission tomography FDG ( Fludeoxyglucose) :

氟代脱氧葡萄糖


http://en.wikipedia.org/wiki/Positron_Emission_Tomography

Background

CT V.S. PET


Technique

Feature Extracting – 1 (on CT) Down sampling (for co-registry) Overlap CT/PET( Down/Up Sampling) Feature Extracting – 2 (on PET) Machine Learning

Technique

Background

CT V.S. PET

Feature Extracting – 1 (on CT) Volume Rectangular Fit Histogram featuresLaws featuresWavelet

：：：

Technique –Feature Extracting – 1 (on CT)

Technique –Feature Extracting – 1 (Wavelet)

M

i

N

j

jiIMxN

Energy1 1

2 ),(1

2D Case

)),(

log(),(1

2

2

1 12

2

normjiI

normjiI

MxNEntropy

M

i

N

j

Technique –Feature Extracting – 1 (Wavelet)

3D Case

M

i

N

j

L

k

kjiIMxNxL

Energy1 1

2

1

),,(1

)),,(log()),,((12

2

1 1 12

2

normkjiI

normkjiI

MxNxLEntropy

M

i

N

j

L

k

Technique –Feature Extracting – 1 (Laws Texture)

M

i

N

j

jiIMxN

Energy1 1

2 ),(1

2D Case

Technique –Feature Extracting – 1 (Laws Texture)

M

i

N

j

jiIMxN

Energy1 1

2 ),(1

3D Case

Down sampling (for co-registry)

Technique –Down sampling (for co-registry)

Raw Image

Low Pass(Average)

High Pass 1(X direction)

High Pass 2(Y direction)

High Pass 3(Corner)

Down sampling (for co-registry)

Technique –Down sampling (for co-registry)

Raw Image

Low Pass(Average)

High Pass 1(X direction)

High Pass 2(Y direction)

High Pass 3(Corner)

Down-samples Image

Feature Extracting – 2 (on PET) SUV Leveled SUV Largest Region’s SUV Other probability features

Technique –Feature Extracting – 2 (on PET)

Feature Extracting – 2 (on PET)


PAWITRA MASA-AH, SOMPHOB SOONGSATHITANON, A novel Standardized Uptake Value (SUV) calculation of PET DICOM files using MATLAB, NEW ASPECTS OF APPLIED INFORMATICS, BIOMEDICAL ELECTRONICS & COMMUNICATIONS

Feature Extracting – 2 (on PET)


Tumor

Level 1

Sub SUV

Level 2

Sub SUV

Level 3

Sub SUV

Level 4

Sub SUV

Level 5

Sub SUV

Feature Feature Feature Feature Feature

Machine Learning Logistic Neural Network SVM (Support Vector Machine) J48

Technique –Machine Learning

Introduction Background Technique Experiments Discussion and Conclusion

Experiments

Sorry, they are now in America

Experiments

Introduction Background Technique Experiments Discussion and Conclusion

Discussion and Conclusion

Discussion: Relation between Image Processing,

DSP, and TWD Kernel of Image Processing Development of Each kernel


Relation between Image Processing, DSP, and TWD TWD:

Analyzing signal with mathematically way, either enhancement of complexity of equation and reducing the amount of computation.

DSP: Dealing the signal with discrete time work.

DIP: Take advantage of these two to give us more

probabilities on studying images.


Kernel of Image Processing Similar to the window function on short

time signal analysis Either Gaussian filter (low pass filtering,

averaging) and edge detection (high pass filtering) are applied to turn into features


Development of Each kernel Low pass filter High pass filter


Development of Each kernel Low pass filter

Down sample ( average) [1 1]

Laws texture (level) [1 2 1], [1 4 6 4 1]

Gaussian blur (normal distribution) [1 8 12 16 12 8 1]


Development of Each kernel High pass filter

Down sample ( change) [1 -1]

Laws texture (edge, ripple) [-1 -2 0 2 1], [1,−4, 6,−4, 1]

Gaussian Laplace Filter Subtract by two Gaussian filter with same

mean, different STD.


Development of Each kernel High pass filter


Conclusion: Image processing is right an example

which implement DSP and TWD. Texture Feature give doctors more clues for

diagnosing More kinds of kernel provide more feature

for machine learning.


time-frequency analysis and wavelet transform oral presentation

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