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2-D Ultrasonic Imaging with Circular Array Data Youli Quan Stanford University Lianjie Huang Los Alamos National Laboratory February, 2007 Objectives • Study of sound-speed reconstruction capability of an efficient time-of-flight tomography method using synthetic data • Lab data sound-speed reconstruction • Reflectivity reconstruction using synthetic data 1 Circular Array • Many research groups have developed circular transducer arrays for acoustic imaging: Schreiman, Gisvold, Greenleaf & Bahn (1984) Waag & Fedewa (2006) Duric, Littrup, Poulo, Babkin, … (2007) • Full apertures to improve image resolution. 2 Ultrasonic Wave Simulation for a Ring Array Simulate ultrasonic wave propagation through numerical breast phantoms. 200 1580 1560 150 y(mm) • 1540 1520 100 1500 1480 50 1460 0 0 50 100 x(mm) 150 200 1440 3 Ultrasonic Wave Simulation for a Ring Array • Use finite-difference time-domain acoustic-wave equation in heterogeneous media. • Source central frequency: 0.5 MHz • Grid size of the numerical phantom: 0.1 mm • 2D grid: 2051 x 2051 • Time signal length: 150 ms • Ring diameter: 20 cm • Take 1 hour to generate 256 common-channel data on a 128-CPU computer cluster. 4 Simulated Ring-Array Data 0 20 Direct Wave Time (microsecond) 40 60 80 100 120 Reflected Wave 140 50 100 150 Channel Number 200 250 5 Data Analysis and Travel-Time Picking 150 1540 0 1530 20 1520 40 y(mm) 1510 100 1500 1490 Time (microsecond) 200 60 80 100 1480 50 120 1470 140 0 1460 0 50 100 x(mm) 150 200 50 100 150 Channel Number 200 250 6 Cross-Correlation Picking and First-Break Picking 1 1 Water Target dT 0.5 Amplitude 0.5 Amplitude Water Target 0 0 -0.5 -0.5 -1 130 132 134 136 138 140 Travel time (microsecond) -1 130 142 132 134 136 138 140 Travel time (microsecond) 142 1 Water Target Time Difference (microsecond) Amplitude 0.5 0 -0.5 Correlation First beak 0.3 0.25 0.2 0.15 0.1 0.05 0 -1 130 132 134 136 138 140 Travel time (microsecond) 142 -0.05 110 115 120 125 130 135 Channel Number 140 145 150 7 Tomographic Reconstruction of Sound-Speed T LS Cd1 / 2T Cd1 / 2 L S CrS0 Cr • Obtain L by tracing bent-rays using a finite-difference scheme to solve the eikonal equation. • Solve the system using an algorithm for sparse linear equations and sparse least squares. 8 Reconstruction of a Circular Object 200 1540 250 0.25 1530 150 y(mm) 1510 100 1500 1490 Transmitter 1520 200 0.2 150 0.15 0.1 100 0.05 1480 50 50 1470 50 100 x(mm) 150 200 200 1460 1540 1520 1530 1510 1510 1500 100 1490 1480 50 50 100 x (mm) 150 200 100 150 Receiver 200 250 1500 1520 150 y (mm) 50 1490 speed (m/s) 0 0 0 1480 1470 1460 1450 1470 1440 1460 1430 0 Given Reconstruction 50 100 x(mm) 150 200 9 Reconstruction of a Square Object 200 1540 250 0.25 1530 150 y(mm) 1510 100 1500 1490 Transmitter 1520 200 0.2 150 0.15 0.1 100 0.05 1480 50 50 1470 50 100 x(mm) 150 200 200 1460 1540 1520 1530 1510 1510 1500 100 1490 1480 50 50 100 x (mm) 150 200 100 150 Receiver 200 250 1500 1520 150 y (mm) 50 sound speed (m/s) 0 0 0 1490 1480 1470 1460 1450 1470 1440 1460 1430 0 Given Reconstruction 50 100 x(mm) 150 200 10 Reconstruction of Small Circular Object 200 250 0.05 1530 100 1500 1490 50 0.03 Transmitter y(mm) 1510 0.04 200 1520 150 150 0.02 0.01 100 0 1480 -0.01 50 1470 0 0 50 100 x(mm) 150 -0.02 200 50 1510 200 100 150 Receiver 200 250 1520 1510 100 1500 50 1495 sound speed (m/s) y (mm) 1500 1505 150 1490 1480 1470 1460 1450 1440 50 100 x (mm) 150 200 1490 1430 0 50 100 x(mm) 150 200 11 Reconstruction of an Off-Center Object 200 1540 250 1530 150 1520 100 1500 1490 0.2 Transmitter 1510 y(mm) 0.25 200 150 0.15 0.1 100 1480 50 0.05 50 1470 0 1460 50 100 x(mm) 150 200 200 150 50 1540 1520 1530 1510 y (mm) 1510 1500 100 1490 1480 50 1470 1460 50 100 x (mm) 150 200 100 150 Receiver 200 250 1500 1520 1490 speed (m/s) 0 0 1480 1470 1460 1450 Given Reconstruction 1440 1430 0 50 100 x(mm) 150 200 12 Reconstruction of a Numerical Phantom 200 250 0 1560 -0.1 1540 150 200 -0.2 100 Transmitter y(mm) 1520 1500 150 -0.3 -0.4 100 1480 -0.5 50 50 1460 0 0 50 100 x(mm) 150 -0.6 200 50 100 150 Receiver 200 250 1530 200 1560 100 1500 1480 50 sound speed (m/s) 1520 y (mm) 1520 1540 150 1510 1500 1490 Given Reconstruction 1460 50 100 x (mm) 150 200 1480 0 50 100 x(mm) 150 200 13 Reconstruction of a Numerical Phantom 200 1560 y(mm) 1520 100 1500 Transmitter 1540 150 250 0 200 -0.2 150 -0.4 100 -0.6 1480 50 1460 0 0 50 100 x(mm) 150 200 50 -0.8 50 100 150 Receiver 200 250 200 1560 1540 150 y (mm) 1520 100 1500 1480 50 1460 50 100 x (mm) 150 200 14 Reconstruction of a Numerical Phantom 200 1560 y(mm) 1520 100 1500 Transmitter 1540 150 250 0 200 -0.2 150 -0.4 100 -0.6 1480 50 1460 0 0 50 100 x(mm) 150 200 50 -0.8 50 100 150 Receiver 200 250 200 1560 1550 150 y (mm) 1540 1530 100 1520 1510 50 1500 1490 50 100 x (mm) 150 200 15 Reconstruction of a Numerical Phantom 200 250 1560 0.2 1520 100 1500 0 Transmitter 150 y(mm) 200 1540 150 -0.2 100 -0.4 1480 50 1460 0 0 50 100 x(mm) 150 50 -0.6 50 200 100 150 Receiver 200 250 200 1560 1540 150 y (mm) 1520 100 1500 1480 50 1460 50 100 x (mm) 150 200 16 Lab Data: First-break Picks 17 Lab Data: Sound-speed Reconstruction 18 Reconstruction of a Numerical Phantom 200 1580 1.2 250 1560 1540 1520 100 1500 0.8 Transmitter y(mm) 150 150 0.6 100 0.4 1480 50 1460 0 0 1 200 50 100 x(mm) 150 200 200 1440 50 0.2 0 50 100 150 Receiver 200 250 1580 1560 y (mm) 150 1540 1520 100 1500 1480 50 1460 50 100 x (mm) 150 200 1440 19 Patient Data: Sound-speed Reconstruction 20 Computational Time Using 1 mm grid spacing, the Tomographic reconstructions with 10 iterations take less than two minutes of CPU times on a Dell xeon 3.0GHz desktop PC. 21 Conclusions • The ring transducer array provides an ideal aperture for sound-speed transmission tomography. • TOF transmission tomography can accurately reconstruct the sound speed for an object > 5 . • For objects < 2 , the reconstruction may indicate the existence of the object, but does not recover the absolute value of the sound speed. • Reflectivity reconstruction has higher resolution than the sound-speed reconstruction 22 Acknowledgements • Work was supported by U.S. DOE Laboratory-Directed Research and Development program. • Data were generated using the computer clusters at Stanford Center for Computational Earth and Environmental Science (CEES). • Numerical breast phantoms were derived from phantom and in-vivo breast data provided by Karmanos Cancer Institute through Neb Duric. 23