Midterm Presentation Performed by: Ron Amit Supervisor: Tanya Chernyakova Semester: Spring Sub-Nyquist Sampling in Ultrasound Imaging

Ultrasound Device: 2

Problem : Modern devices require large number of receivers Acoustic pulses are of high bandwidth Typical Nyquist rate is 20 MHz * Number of receivers Large amount of data must be processed High computational cost 3

4 Solution : Reduce sample rate, while still extracting the same required information for image reconstruction

FRI Model: 5

Single receiver solution : Unknown parameters are extracted from low rate samples. 6

Multichannel Sampling Scheme : Different sampling scheme for a single receiver, using bank of integrators 7

Problem : Low SNR of received signal at a single receiver. Solution : Use array of receivers and combine the received signals – Beamforming process. Beamformed signal has improved SNR Represents reflections from a single angle – forming an image line 8

Beamforming : 9

Compressed Beamforming : Combines Beamforming and sampling process. Received signals are sampled at Sub-Nyquist rate The scheme’s output is a group of Beamformed signal ‘s Fourier coefficients Digital processing extracts the Beamformed signal parameters 10

Using modulation with analog kernels and integration First Scheme : Problem : Analog kernels are complicated for hardware implementation 11

Simplified Scheme : Based on approximating each received signal by only Ki Fourier coefficients Each received signal is filtered by a simple analog filter Linear transformation on the samples provides the Beamformed signal Fourier coefficients 12

13 Analog Processing Sub – Nyquist Sampling Receiver Elements Low Rate Samples Digital Processing Amplitudes and delays of reflections Image Reconstruction Block Diagram :

14 Image Construction: Standard Image Construction: Delays and amplitudes are translated to a stream of modulated pulses Hilbert transform is used for un-modulation The data points in 120 image lines (angles) are interpolated to a 2-D Cartesian Image Problem: The standard process is complicated and slow 2-D interpolation is very slow Doesn't use the fact that Xampled Images are mostly zero Modulation and Un-modulation is unnecessary

15 Alternative Image Construction: Build signals with un-modulated pulse shape Only one dimensional interpolation: in angle axis Finds nearest Cartesian coordinates for every data point (which is in Polar coordinates ) and place the amplitude (nearest neighbor method) Computation is done only for non-zero data points Goal: Faster image construction from Xampled data Solution :

16 Alternative Image Construction: Average runtime: 4 seconds Average runtime: 0.5 seconds Standard Image Construction: Almost identical image! Reduced computation complexity!

17 Project Goals : Main goal: Prove the preferability of the Xampling method for Ultrasound devices Sub goals: Alternative image reconstruction Optimize algorithm and improve runtime Explore hardware implementation

18 Semester 1: Understand and run current code Improvement: Image construction from pulses Lighter OMP algorithm Semester 2: Algorithm optimization: Flow graph algorithm Complexity analysis of subroutines Runtime optimization System analysis : How to implement on processer platform for maximal performance Mission Plan: