Ultrasonic Attenuation TomographyBased on Log-Spectrum Analysis

Radovan Jiřík, Rainer Stotzka, Torfinn Taxt

Brno University of TechnologyDepartment of Biomedical EngineeringBrno, CZECH REPUBLIC

University of BergenDepartment of BiomedicineBergen, NORWAY

Forschungszentrum KarlsruheInstitute for Data-Processing and ElectronicsEggenstein, GERMANY

1. Introduction

Aim:

ultrasonic attenuation tomographyfor breast cancer diagnosis using

1. Introduction

B-mode ultrasonic imaging• low spatial resolution• low contrast

Ultrasound computed tomography• more data available• more complicated acquisition and signal processing

Ultrasound attenuation imaging• att. coef. closely related to tissue type and pathology• tomography setup possible for mammography• correction of reflection tomography images• standalone imaging modality

1. Introduction

Main idea: processing of reflected / scattered signal

sendingtransducer

l

receivingtransducer

s(t)

{tl = l / c

t

Initial study presented

{

undirected beam

2. Model of RF signal

Directly transmitted signalsendingtransducer

l

receivingtransducer

s(t)

t

{tl = l / c

FFT

S(,l)

nattenuatio

lil

pulse

eeGlS ),(2)(),(

mean attenuation coefficient

s(t)

t

2. Model of RF signal

Reflected / scattered signalsendingtransducer

receivingtransducer

{FFT

S(,l1+l2)

nattenuatio

llill

pulse

eeGllS ),(2)(

2121

21

)(),(

l1

l2

3. Method

Segment of reflected / scattered signal - amplitude spectrum:

2)(

21

21

)(),(ll

eGllS

Log-spectrum:

2

)()(log),(log 2121 llGllS

Modified log-spectrum:

2

)(),(log 2121 llllSM

Linear regression => (mean attenuation coefficient along the path l1+l2)

0

0

3. Method

x

y{

1

{

n

{

2

{

3

In the end – mean of thecumulated values calculated

For each pixel - all combinations of sending and receiving positions

3. Method

Method analysis

• All segments with the contribution of the computed pixel cumulated

• Contribution of other pixels does not average out• Values shifted closer to the mean attenuation

coefficient in the image• Influence of neighboring pixels

• Estimation of : for non-sparse reflectors / scatterers log-spectrum not a linear function, but still a monotonous function

i

4. Results

Standard unfiltered backprojection

New attenuation imaging technique

5. Conclusion

• Not only directly transmitted signal processed, reflected / scattered signal used in addition => significantly more data

• Attenuation images with less geometry distortion than the backprojection algorithm

• Simplifying assumptions used

Further research• huge set of linear / nonlinear equations• “Filtered backprojection” algorithm for non-straight

propagation lines ???• More complete model (non-sparse reflectors / scatterers)