Sub-sample displacement estimation from digitized ultrasound RF signals using multi-dimensional polynomial fitting of
Reza Zahiri Azar1, Orcun Goksel, Septimiu E Salcudean
1Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada. zahiri@ece.ubc.ca
Summary
This study introduces advanced 2-D and 3-D polynomial fitting for ultrasound motion estimation, significantly improving sub-sample accuracy. The new method reduces estimation errors by over ten times compared to traditional 1-D fitting.
Area of Science:
- Medical Imaging
- Ultrasound Technology
- Signal Processing
Background:
- Ultrasound radiofrequency (RF) signal analysis commonly uses cross-correlation for motion and delay estimation.
- Sub-sample accuracy in motion estimation is typically achieved through interpolation of discrete pattern-matching functions.
- Previous methods relied on 1-D fitting, applied independently along different axes, limiting accuracy in multi-dimensional scenarios.
Purpose of the Study:
- To investigate the efficacy of 2-D and 3-D polynomial fitting for enhanced sub-sample motion and delay estimation in ultrasound.
- To quantify and compare the estimation errors of multi-dimensional polynomial fitting against traditional 1-D fitting methods.
- To evaluate the performance of these techniques in both simulated and experimental ultrasound data.
Main Methods:
- Utilized Field II for noise-free simulations of 2-D translational motions and 1% axial strain.
- Employed 2-D and 3-D polynomial fitting, specifically quartic spline polynomials, for interpolation and estimation.
- Conducted experiments using a commercial ultrasound machine with a linear array transducer.
Main Results:
- In 2-D simulations, quartic spline fitting resulted in axial bias <0.2% and lateral bias <0.4% of sample spacing.
- Maximum standard deviations in simulations were approximately 1% of sample spacing for both axial and lateral directions.
- Experimental results showed over a tenfold reduction in bias compared to 1-D fitting, with axial bias <458 nm and lateral bias <6.27 μm.
Conclusions:
- 2-D and 3-D polynomial fitting offer superior accuracy for sub-sample motion estimation in ultrasound compared to 1-D methods.
- The proposed multi-dimensional fitting approach significantly reduces estimation bias and standard deviation in both simulated and real-world ultrasound data.
- This advancement has the potential to improve the precision of various ultrasound-based diagnostic and measurement techniques.
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