Performed by: Ron Amit Supervisor: Tanya Chernyakova In cooperation with: Prof. Yonina Eldar

1. Sub-Nyquist Sampling in Ultrasound Imaging Performed by: Ron Amit Supervisor: Tanya Chernyakova In cooperation with: Prof. YoninaEldar Part A Final Presentation Semester: Spring 2012

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

3. Introduction

4. Ultrasound Imaging Introduction

5. Beamforming Introduction

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 Introduction

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

8. Project Goals • 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

10. FRI Model • Theoretical lower bound of sample rate: Background

11. Unknown Phase • Define: Background

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

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

14. Compressed Beamforming • 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. Background

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

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

17. Recovery Method

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

19. Parameter Recovery • Problem : Recover and from samples • Time delay : • Amplitude and phase: • Complex samples: - Partial group of the Beamformed signal’s Fourier Coefficients • The relation shown in [1]: Recovery Method

20. Compressed Sensing Formulation Time quantization: Number of times samples: Equation Set: , j=1,..,K Recovery Method

21. Define : Compressed Sensing Formulation Equation Set: Matrix Form: Problem: = V, unknown [KxN] – Partial DFT Matrix K << N Recovery Method

22. OMP Algorithm Problem: = V, unknown Sparsity assumption: OMP Solves : , such that OMP with L=25: Standard Image: Recovery Method

23. New Approach • The signal is reconstructed by incorporating the pulse shape • Namely, passing trough a band-pass filter: • Conceptual Change: • The signal of interest is and not . • need to be reconstructed correctly only in the pulse pass-bandbandwidth . Recovery Method

24. New Approach • Assume includes all the Fourier coefficients in the pulse bandwidth: • Any for which the Fourier coefficients in the pulse bandwidth are equal to will yield perfect reconstruction. • Equivalent condition: = V exactly. Recovery Method

25. Proposed Solution Solve: = V Possible Solution: = Proof: • Simple solution - easy to calculate • Equivalent to building using only the sampled frequencies Recovery Method

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

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

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

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

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

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

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

33. ImageConstruction

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

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

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

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

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

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

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

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

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

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

44. Summary

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

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. 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. [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