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Sub- Nyquist Sampling in Ultrasound Imaging. Performed by: Ron Amit Supervisor: Tanya Chernyakova In cooperation with: Prof. Yonina Eldar. Part A Final Presentation Semester: Spring 2012. Agenda. Introduction Project Goals Background Recovery Method Image Construction Summary
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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
Agenda • Introduction • Project Goals • Background • Recovery Method • Image Construction • Summary • Future Goals
Ultrasound Imaging Introduction
Beamforming Introduction
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
Solution • Develop a low rate sampling scheme based on knowledge about the signal structure Introduction
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
FRI Model • Theoretical lower bound of sample rate: Background
Unknown Phase • Define: Background
Block Diagram Sampling Scheme Recovery Image Construction Low Rate Samples Receiver Elements Background
Single Receiver Xample Scheme • Unknown parameters are extracted from low rate samples. Background
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
Compressed Beamforming First Sampling Scheme : Using analog kernels and integrators Problem : Analog kernels are complicated for hardware implementation Background
Compressed Beamforming Simplified Sampling Scheme : • Based on approximation • One simple analog filter per receiver • Linear transformation applied on samples Background
Block Diagram Sampling Scheme Recovery Image Construction Low Rate Samples Receiver Elements
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
Compressed Sensing Formulation Time quantization: Number of times samples: Equation Set: , j=1,..,K Recovery Method
Define : Compressed Sensing Formulation Equation Set: Matrix Form: Problem: = V, unknown [KxN] – Partial DFT Matrix K << N Recovery Method
OMP Algorithm Problem: = V, unknown Sparsity assumption: OMP Solves : , such that OMP with L=25: Standard Image: Recovery Method
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
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
Proposed Solution Solve: = V Possible Solution: = Proof: • Simple solution - easy to calculate • Equivalent to building using only the sampled frequencies Recovery Method
Proposed Solution - Result Using all the 361 Fourier coefficients in the pulse bandwidth: Recovery Method
Proposed Solution - Result Proposed Solution (using 722 real samples): Standard Image (using 1662 real samples ): Recovery Method
Sub - Sample Can a smaller number of samples be used? • Using 100 out of 361 coefficients: Recovery Method
Artifact • Using 100 out of 361 coefficients: Recovery Method
Artifact: Solution • Using 100 weighted coefficients: Non-Ideal Band Pass: Recovery Method
Proposed Solution - Result • Proposed Solution , with weights (using 200 real samples): OMP (using 200 real samples): Recovery Method
Proposed Solution - Result • Proposed Solution , with weights (using 200 real samples): Standard Image (using 1662 real samples ): Recovery Method
Block Diagram Sampling Scheme Recovery Image Construction Low Rate Samples Receiver Elements
Image Construction Signal Creation: For each image line (angle), create signal from estimated parameters Interpolation: Interpolate Polar data to full Cartesian grid Image Construction
Signal Creation • Standard method – Use Hilbert transform to cancel modulation • In signal creation, pulse envelope can be used beforehand Image Construction
Signal Creation • Convolution with pulse envelope • Problem: Image is blurred • Estimated Phase is needed for a clear image Image Construction
Signal Creation Signal Model: Using: } שלב ביניים: } Convolution Form: Image Construction
Image Construction Signal Creation: For each image line (angle), create signal from estimated parameters Interpolation: Interpolate Polar data to full Cartesian grid Image Construction
2D Interpolation • 2D Linear interpolation • High quality image, but very slow Image Construction
Nearest Neighbor Interpolation • Each Cartesian gets the value of the nearest polar data point • Lower quality image, but fast Image Construction
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
Image Construction - Results My method: Standard Imaging: • Almost identical images • Significant runtime reduction Image Construction
Summary Achievements: • New recovery method • Significantly faster recovery runtime • Very simple hardware implementation • Much better image quality • Significantly faster image construction runtime
Future Goals • Improve the simplified sampling scheme • Cooperation with GE Healthcare • Build a demo which shows the efficiency of the Sub- Nyquist method
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