Ultrasonic Attenuation Tomography Based on Log-Spectrum Analysis Radovan Jiřík, Rainer Stotzka, Torfinn Taxt Brno University of Technology Department of Biomedical Engineering Brno, CZECH REPUBLIC University of Bergen Department of Biomedicine Bergen, NORWAY Forschungszentrum Karlsruhe Institute for Data-Processing and Electronics Eggenstein, GERMANY

1. Introduction Aim: ultrasonic attenuation tomography for 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 sending transducer l receiving transducer s(t) { t l = l / c t Initial study presented { undirected beam

2. Model of RF signal Directly transmitted signal sending transducer l receiving transducer s(t) t { t l = l / c FFT S( ,l) mean attenuation coefficient

s(t) t 2. Model of RF signal Reflected / scattered signal sending transducer receiving transducer { FFT S( ,l 1 +l 2 ) l1l1 l2l2

3. Method Segment of reflected / scattered signal - amplitude spectrum: Log-spectrum: Modified log-spectrum: Linear regression =>(mean attenuation coefficient along the path l 1 +l 2 ) 00   00  

3. Method x y { { { { In the end – mean of the cumulated 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

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)