1. Performed by: Ron Amit Supervisor: Tanya Chernyakova In cooperation with: Prof. Yonina Eldar 1 Part A Final Presentation Semester: Spring 2012

2. Agenda Introduction Project Goals Background Recovery Method Image Construction Summary Future Goals 2

3. Introduction 3

4. Ultrasound Imaging 4Introduction

5. 5 Beamforming

6. Problem Typical Nyquist rate is 20 MHz * Number of transducers * Number of image lines Large amount of data must be collected and processed in real time 6Introduction

7. Solution Develop a low rate sampling scheme based on knowledge about the signal structure 7Introduction

8. 8 Main goal : Prove the preferability of the Xampling method for Ultrasound imaging Part A: Improve recovery method Improve image construction runtime Project Goals

9. Background 9

10. FRI Model 10Background

11. Unknown Phase 11Background Define:

12. 12 Sampling Scheme Receiver Elements Low Rate Samples Recovery Image Construction Background Block Diagram

13. Single Receiver Xample Scheme Unknown parameters are extracted from low rate samples. 13 Background

14. Combines Beamforming and sampling process. Samples are a group of Beamformed signal’s Fourier coefficients. Sampling at Sub-Nyquist rate is possible. Digital processing extracts the Beamformed signal parameters. 14 Compressed Beamforming Background

15. Using analog kernels and integrators First Sampling Scheme : Problem : Analog kernels are complicated for hardware implementation 15Background Compressed Beamforming

16. Simplified Sampling Scheme : Based on approximation One simple analog filter per receiver Linear transformation applied on samples 16Background Compressed Beamforming

17. Recovery Method 17

18. 18 Sampling Scheme Receiver Elements Low Rate Samples Recovery Image Construction Block Diagram

19. Recovery Method19 Parameter Recovery

20. Compressed Sensing Formulation Time quantization: Number of times samples: Equation Set: Recovery Method20

21. Recovery Method21 Matrix Form: Compressed Sensing Formulation Equation Set: K << N

22. Recovery Method22 OMP Algorithm Standard Image: OMP with L=25:

23. Recovery Method23 New Approach

24. Recovery Method24 New Approach

25. Proposed Solution Possible Solution: Proof : Recovery Method

26. 26 Using all the 361 Fourier coefficients in the pulse bandwidth: Proposed Solution - Result Recovery Method

27. 27 Proposed Solution - Result Proposed Solution (using 722 real samples): Standard Image (using 1662 real samples ): Recovery Method

28. 28 Sub - Sample Using 100 out of 361 coefficients: Can a smaller number of samples be used? Recovery Method

29. 29 Artifact Using 100 out of 361 coefficients: Recovery Method

30. 30 Artifact: Solution Non-Ideal Band Pass: Using 100 weighted coefficients: Recovery Method

31. 31 Proposed Solution, with weights (using 200 real samples): OMP (using 200 real samples): Proposed Solution - Result Recovery Method

32. 32 Proposed Solution, with weights (using 200 real samples): Proposed Solution - Result Standard Image (using 1662 real samples ): Recovery Method

33. Image Construction 33

34. 34 Sampling Scheme Receiver Elements Low Rate Samples Recovery Image Construction Block Diagram

35. Image Construction35 Image Construction 1. Signal Creation: For each image line (angle), create signal from estimated parameters 2. Interpolation : Interpolate Polar data to full Cartesian grid

36. Image Construction36 Signal Creation Standard method – Use Hilbert transform to cancel modulation In signal creation, pulse envelope can be used beforehand

37. Image Construction 37 Signal Creation Convolution with pulse envelope Problem: Image is blurred Estimated Phase is needed for a clear image

38. Image Construction38 Signal Creation Signal Model: Using: שלב ביניים : Convolution Form:

39. Image Construction39 Image Construction 1. Signal Creation: For each image line (angle), create signal from estimated parameters 2. Interpolation : Interpolate Polar data to full Cartesian grid

40. Image Construction40 2D Interpolation 2D Linear interpolation High quality image, but very slow

41. Image Construction41 Nearest Neighbor Interpolation Each Cartesian gets the value of the nearest polar data point Lower quality image, but fast

42. Image Construction42 My method Interpolate only in the angle axis (1D interpolation) Place each polar data point in the nearest point on the Cartesian grid

43. Image Construction43 Image Construction - Results Almost identical images Significant runtime reduction My method: Standard Imaging:

44. Summary 44

45. 45 New recovery method Significantly faster recovery runtime Very simple hardware implementation Much better image quality Significantly faster image construction runtime Achievements: Summary

46. 46 Future Goals Improve the simplified sampling scheme Cooperation with GE Healthcare Build a demo which shows the efficiency of the Sub- Nyquist method

47. 47 References: [1] N. Wagner, Y. C. Eldar and Z. Friedman, "Compressed Beamforming in Ultrasound Imaging", IEEE Transactions on Signal Processing, vol. 60, issue 9, pp.4643-4657, Sept. 2012. "Compressed Beamforming in Ultrasound Imaging" [2] Ronen Tur, Y.C. Eldar and Zvi Friedman, “Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging”, IEEE Trans. Signal Process., vol. 59, no. 4, pp. 1827-1842, 2011 [3] K. Gedalyahu, R. Tur and Y.C. Eldar, “Multichannel Sampling of Pulse Streams at the Rate of Innovation”, IEEE Trans. Signal Process., vol. 59, no. 4, pp. 1491-1504, 2011