part 1 lab 8

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Velez-Colon | EE 454

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Jose J. Velez-Colon

Dr. Won

EE 454

Tuesday, September 1, 2009

*There are 2 documents: (1) Transformations on B-Mode 2-D Images and (2) Doppler.

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TRANSFORMATIONS ON B-MODE 2-DIMAGES

Questions.

1.What variables are stored in the file?The following variables are stored in the file carotid1:

Name Size Bytes Class Attributes

bmode_rf 1816x312 4532736 double

fc 1x1 8 doubleposx_bmode 312x1 2496 double

2. Which variable is most likely to be the image data itself? Why?

The bcmode_rf ' variable should be the image because it is the only variable that is 2

dimensional.

3.View the image by typing image(bmode_rf). How well are you able to make out anystructures?

It is nearly impossible to see the structures. Perhaps, a trained eye could see them.

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4. Obtain the envelope of the raw image data by constructing the analytic signal img. Remember,

this signal contains the Hilbert transform of the raw data. Use the command hilbert, andpay

attention to what the output of this function is.

After using Hilbert and taking the magnitude of the result we get:

Two examples of the envelope of the image are below:

Hilbert without normalization

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Plot the histogram

Envelope of the image

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Gaussian Distribution without logarithmic compression.

PixelValues

Histogram

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Plot the histogram after logarithmic compression.

Compute the axial distance and plot spatial map.

The axial distance = 3.9500e-005

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Histogram after Logarithmic Compression

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spatial map

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Spatial Map usign logarithmic compression

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Plot of the image using small range.

range .5 to 15 without logarithmic compression

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range .5 to 15 with logarithmic compression

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Now we will repeat the exercise for carotid5.mat:

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Hilbert without normalization

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Envelope of the image

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Gaussian Distribution without logarithmic compression.

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Histogram

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Compute the axial distance and plot:

The axial distance = 3.9500e-005

spatial map

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Spatial Map usign logarithmic compression

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Histogram after Logarithmic Compression

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range .5 to 15 without logarithmic compression

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range .5 to 15 with logarithmic compression

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MATLABCODE

clc; clear; close all;load('carotid5') % just change this to carotid9 to get the other results for

% part 2 Didnt want to waste paperfigure(1)

image(bmode_rf);

%Obtain the envelope of the raw image data by constructing the analytic

signal img. Remember,%this signal contains the Hilbert transform of the raw data. Use the command

hilbert, and%pay attention to what the output of this function is.x = hilbert(bmode_rf);figure(2)a=abs(x);imagesc(a)title('Hilbert without normalization')

% normalizationamax = max(max(a));amin = min(min(a));

normalizeImage= (a / (amax-amin)) - amin;figure(3)imagesc(normalizeImage)colormap bonetitle('Envelope of the image');

%plot the histogram of normalizeImagebins= linspace(0,50,50);% 50 equally spaced

figure(4)hist(normalizeImage, bins)axis([-.5 .5 0 1850]);xlabel('Gaussian Distribution without logarithmic compression.');ylabel('Pixel Values');title('Histogram');

k=20; % scaling constantc=.5;% compresion constantlogcompression = k * exp( log(normalizeImage) );% what I think is logarithmic

compression...

figure(5)

hist(logcompression, bins)axis([-.5 .5 0 1850]);title('Histogram after Logarithmic Compression');% Axial Distance% lambda = c/f where c is velocity and f is frequency and lambda is axial% distance.c= 1580;%m/s

f=40e6;

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lambda=c/f

% spatial mapc=c*100;%cm/sT=1/f;%sampling periodspatialMap = a(1,:) * c*T/2;figure(6)

imagesc(spatialMap,posx_bmode,a)title('spatial map')

figure(7)spatialMap2 = logcompression(1,:) * c*T/2;imagesc(spatialMap2,posx_bmode,a)title('Spatial Map usign logarithmic compression')

figure(8)imagesc(a(.5:.1:15));title('range .5 to 15 without logarithmic compression')

figure(9)imagesc(logcompression(.5:.1:15))title('range .5 to 15 with logarithmic compression')

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DOPLER EFFECT

Questions.

1. What variables are contained in this file?Name Size Bytes Class Attributes

bmode_rf 1816x188 2731264 double

doppler_rf 1816x90x15 19612800 doublefc 1x1 8 double

fc_dop 1x1 8 doubleposx_bmode 188x1 1504 double

posx_dop 90x1 720 doubleprf 1x1 8 double

2.

Envelope Detection:

Image after taking the hilbert and magnitude

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Logarithmic Compression from .5 to 15

Doppler Images:

3. Look through the images over time. Do you see any difference?I look at it at a glance and all the images look alike.

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From left to right, images with respect to time:

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4 5 6

You can notice small movements in the images.

After the filter was applied I looked though the image to get:

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image after filtering

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The sum of all doppler powers together:

dopplerPower 2.3325e+007

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8 Doppler Power

Doppler Power Spatial Map

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MATLABCODE

clc;clear; close all;load('carotid9.mat');x = hilbert(bmode_rf);x = abs(x);

figure(1)imagesc(x)title('Image after taking the hilbert and magnitude');

% envelope detectionxmax = max(max(x));xmin = min(min(x));normalizeImage = abs(( x / (xmax - xmin) ) - xmin);

figure(2)imagesc(normalizeImage)title('envelope detector')colormap bone;

% Logarithmic Compression

figure(3)k = 20;c = .1;logCompression = k * exp( log (normalizeImage ) );imagesc((logCompression))

figure(4)imagesc(logCompression(.5:15))

%I only used this code to view the images of the doppler once, then I%commented it out.

% for j=3:15% figure(j)% copyDopler=[];% copy1Dopler=doppler_rf(:,:,j);% imagesc(copy1Dopler)%

% end

% filtering with butterworh

doppler_rf = doppler_rf (.5:15) ;ORDER = 2;% by recomendation of the m file.

FCUTOFF = .5;

output=URIIIRfilter(doppler_rf,ORDER,FCUTOFF);

output= real(output);% filtering ends

% looking througth the volume after filteringfigure(5)

imagesc(output)title('image after filtering')

% analytical signal of each image (hilbert)

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%calculating all analytical signalsresult=[];for i=1:187,

analyticalSignal1=[];% erase the dataanalyticalSignal2=[];% erase the data

analyticalSignal1=hilbert(bmode_rf(:,i));analyticalSignal2=conj(hilbert(bmode_rf(:,i+1)));

computation = analyticalSignal1 .* analyticalSignal2;result=[result computation];% store all the computations to calculate

the phase later.

end

% angle returns the phase angle in radians

imaginary = imag(result);realPart = real(result);phaseSum = sum(atan(imaginary/realPart));

% doppler velocityv = (c * fc / (4*pi*fc_dop)) .* phaseSum;

% doppler powerresult2=[];for i=1:187,

analyticalSignal1=[];% erase the dataanalyticalSignal2=[];% erase the data

analyticalSignal1=hilbert(bmode_rf(:,i));analyticalSignal2=conj(hilbert(bmode_rf(:,i)));computation = analyticalSignal1 .* analyticalSignal2;result2=[result2 computation];% store all the computations to calculate

the phase later.

end% doppler power additiondopplerPower2 =cumsum(result2);dopplerPower2 =dopplerPower2(end);

% doppler power for spatial mapdopplerPower = sum(result2);figure(6)bar(dopplerPower)title('Doppler Power')

%spatial mapc = 1540*100;

fs = 40e6;T = 1/fs;spatialMap = dopplerPower(1,:)*c*T/2;figure(7)imagesc(spatialMap,posx_bmode,dopplerPower)title('Doppler Power Spatial Map')

Thank you Dr Won. I have learned more in the past quarters with you than in the past 5 years!

I hope you have a good vacation.

part 1 lab 8

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