Sub-sample displacement estimation from digitized ultrasound RF signals using multi-dimensional polynomial fitting of the cross-correlation function

Azar, Reza Zahiri; Göksel, Orçun; Salcudean, Septimiu E.

doi:10.1109/tuffc.2010.1708

Cited by 46 publications

(35 citation statements)

References 58 publications

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“…This effect can be appreciated in Figure 8, where vertically stripped patterns are visible in the magnitude and angle estimates for the PSF_1Dpar en conv_1Dpar methods. These patterns originate from the inaccurate lateral displacement estimates in regions of subsample axial displacements, as also reported earlier [33]. The benefit of using 1D parabolic interpolation is the low computational cost, whereas 2D cubic interpolation increases computational time.…”

Section: Discussionsupporting

confidence: 60%

“…Many other studies have investigated the use of other shapes and functions, such as cosine, parabolic or spline [25,33,35,51,52], most often in 1D. However, none of these interpolators have been studied before in the context of the proposed methodology, i.e., in combination with the freedom of choosing the beamforming grid and thereby influencing the CCF shape.…”

Section: Discussionmentioning

confidence: 99%

“…Two types of interpolation were used: 1D parabolic fitting in each direction of the CCF independently, since it is one of the most often used interpolators in ultrasound applications as described in the Introduction, and 2D cubic interpolation, where a joint estimation of subsample displacement in both directions was obtained. The parabolic fitting is solved analytically using the commonly applied three-point parabola fitting [25,33]. 2D cubic interpolation was performed with a resulting effective upsampling factor of 10 and 1000 in the first and second step of the algorithm, respectively.…”

Section: Multi-step Speckle Tracking Settingsmentioning

confidence: 99%

“…For conventionally acquired, line-by-line data, interpolation of the pattern matching function is often applied to acquire subsample displacement estimates [25,33,34]. The sampling grid for conventional data is predefined, with normally a line distance equal to the pitch and an axial grid spacing with typically four samples per wavelength.…”

Section: Introductionmentioning

confidence: 99%

“…A predefined shape or curve, often parabolic or cosine [34,35], is assumed and fitted to the peak of the function, either in each direction of the 2D function independently [25,35], or by fitting in 2D to obtain a joint estimate of subsample displacement in both directions. Zahiri Azar et al [33] investigated 2D polynomial fitting to get a joint estimation of subsample displacement and showed significant improvements in terms of bias and standard deviation (SD) compared to the commonly used 1D parabolic and cosine fitting. Interpolating in between echo signals is also often applied to reduce the error of the subsample displacement estimates [25,36,37].…”

Section: Introductionmentioning

confidence: 99%

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A PSF-Shape-Based Beamforming Strategy for Robust 2D Motion Estimation in Ultrafast Data

et al. 2018

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This paper presents a framework for motion estimation in ultrafast ultrasound data. It describes a novel approach for determining the sampling grid for ultrafast data based on the system's point-spread-function (PSF). As a consequence, the cross-correlation functions (CCF) used in the speckle tracking (ST) algorithm will have circular-shaped peaks, which can be interpolated using a 2D interpolation method to estimate subsample displacements. Carotid artery wall motion and parabolic blood flow simulations together with rotating disk experiments using a Verasonics Vantage 256 are used for performance evaluation. Zero-degree plane wave data were acquired using an ATL L5-12 (f c = 9 MHz) transducer for a range of pulse repetition frequencies (PRFs), resulting in 0-600 µm inter-frame displacements. The proposed methodology was compared to data beamformed on a conventionally spaced grid, combined with the commonly used 1D parabolic interpolation. The PSF-shape-based beamforming grid combined with 2D cubic interpolation showed the most accurate and stable performance with respect to the full range of inter-frame displacements, both for the assessment of blood flow and vessel wall dynamics. The proposed methodology can be used as a protocolled way to beamform ultrafast data and obtain accurate estimates of tissue motion.

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Section: Discussionsupporting

confidence: 60%

Section: Discussionmentioning

confidence: 99%

Section: Multi-step Speckle Tracking Settingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A PSF-Shape-Based Beamforming Strategy for Robust 2D Motion Estimation in Ultrafast Data

et al. 2018

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Ultrasonic Methods for Assessment of Tissue Motion in Elastography

Jiang

Peng

2018

Ultrasound Elastography for Biomedical Applications and Medicine

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Biplanar ultrasound investigation of in vivo Achilles tendon displacement non-uniformity

2018

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The Achilles tendon is a common tendon for the medial and lateral gastrocnemius and soleus muscles. Non‐uniform Achilles tendon regional displacements have been observed in vivo which may result from non‐uniform muscle loading and intratendinous shearing. However, prior observations are limited to the sagittal plane. This study investigated Achilles tendon tissue displacement patterns during isometric plantarflexor contractions in the coronal and sagittal planes. Fourteen subjects (5 female, 9 male, 26 ± 3 year) performed maximal isometric plantarflexor contractions with the knee in full extension and flexed to 110°. An ultrasound transducer positioned over the free Achilles tendon collected beam formed radio frequency (RF) data at 70 frames/s. Localized tissue displacements were analyzed using a speckle tracking algorithm. We observed non‐uniform Achilles tendon tissue displacements in both imaging planes. Knee joint posture had no significant effect on tissue displacement patterns in either imaging plane. The non‐uniform Achilles tendon tissue displacements during loading may arise from the anatomical organization of the sub‐tendons associated with the three heads of the triceps surae. The biplanar investigation suggests that greatest displacements are localized to tissue likely to belong to soleus subtendon. This study adds novel information with possible implications for muscle coordination, function, and muscle‐tendon injury mechanisms.

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Sub-sample displacement estimation from digitized ultrasound RF signals using multi-dimensional polynomial fitting of the cross-correlation function

Cited by 46 publications

References 58 publications

A PSF-Shape-Based Beamforming Strategy for Robust 2D Motion Estimation in Ultrafast Data

A PSF-Shape-Based Beamforming Strategy for Robust 2D Motion Estimation in Ultrafast Data

Ultrasonic Methods for Assessment of Tissue Motion in Elastography

Biplanar ultrasound investigation of in vivo Achilles tendon displacement non-uniformity

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