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

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

Introduction 3

Ultrasound Imaging 4Introduction

5 Beamforming

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

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

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

Background 9

FRI Model 10Background

Unknown Phase 11Background Define:

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

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

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

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

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

Recovery Method 17

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

Recovery Method19 Parameter Recovery

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

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

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

Recovery Method23 New Approach

Recovery Method24 New Approach

Proposed Solution Possible Solution: Proof : Recovery Method

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

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

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

29 Artifact Using 100 out of 361 coefficients: Recovery Method

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

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

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

Image Construction 33

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

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

Image Construction36 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 Construction38 Signal Creation Signal Model: Using: שלב ביניים : Convolution Form:

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

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

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

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

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

Summary 44

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

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 , Sept "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 , 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 , 2011