A magnetic phantom technique for investigating structural effects on quantitative ultrasound parameters.

Media that contain ultrasound scatterers arranged in a regular spatial distribution can be considered as structured. Structural effects affect quantitative ultrasound parameters that reflect the microstructure properties. Prior studies examined structural effects using simulations or phantoms with fixed microarchitecture, focusing on a limited set of ultrasound parameters, with limited attention given to their underlying physical significance. This study aims to investigate the concordance of the physical interpretations of multiple quantitative ultrasound parameters experimentally by introducing a phantom type with an adjustable microarchitecture. The phantom consists of an aqueous solution containing superparamagnetic microspheres, acting as scatterers. The spatial arrangement of the magnetic particles is modified by applying an external magnetic field, therefore changing the degree of structure of the phantom. Quantitative ultrasound parameters are estimated in three different configurations: the magnetic field intensity is varied over time, strength, and orientation. In each experiment, the backscatter coefficient and the envelope quantitative ultrasound parameters are successfully extracted (R2 ≈ 0.94). Their physical interpretations are supported by microphotographs and geometrical considerations through concordant hypotheses. This study paves the way for the use of magnetic phantoms. This methodology could be followed to validate theoretical scattering models and the physical meanings of quantitative ultrasound parameters.

Back-propagation beamformer design for motion estimation in echocardiography.

Transverse oscillation (TO) techniques have shown their potential for improving the accuracy of local motion estimation in the transverse direction (i.e., the direction perpendicular to the beam axis). The conventional design of TOs in linear geometry, which is based on the Fraunhofer approximation, relates point spread function (PSF) and apodization function through a Fourier transform. Motivated by the adaptation of TOs in echocardiography, we propose a specific beamforming approach based on back-propagation (BP) to build TOs in sector-shaped geometry. Numerical simulations and experimental data give a comparison between proposed and conventional beamforming for TOs. The accuracy is first quantified by comparing the generated and theoretical PSF using the root mean square error (RMSE) and shows that BP-based beamforming approximates the desired TOs more closely than the conventional approach. Motion estimation is then evaluated. The axial and lateral displacements are within the range [0-0.6] mm and [0°-6.4°], respectively, which correspond to 0.8 times the axial (0.73 mm) and lateral (8°) wavelengths. The result shows that the proposed method yields a clear improvement for lateral displacements, by reducing the error by 28.6% compared with Fourier transform-based beamforming, while maintaining the same error for axial motion estimation. Experimental measurements are discussed to complete this study and confirm that BP-based beamforming leads to better controlled TO images than conventional Fourier-based beamforming.

OntoVIP: an ontology for the annotation of object models used for medical image simulation.

This paper describes the creation of a comprehensive conceptualization of object models used in medical image simulation, suitable for major imaging modalities and simulators. The goal is to create an application ontology that can be used to annotate the models in a repository integrated in the Virtual Imaging Platform (VIP), to facilitate their sharing and reuse. Annotations make the anatomical, physiological and pathophysiological content of the object models explicit. In such an interdisciplinary context we chose to rely on a common integration framework provided by a foundational ontology, that facilitates the consistent integration of the various modules extracted from several existing ontologies, i.e. FMA, PATO, MPATH, RadLex and ChEBI. Emphasis is put on methodology for achieving this extraction and integration. The most salient aspects of the ontology are presented, especially the organization in model layers, as well as its use to browse and query the model repository.

Complete Complementary Coded Excitation Scheme for SNR Improvement of 2D Sparse Array Ultrasound Imaging.

Driving the numerous elements of 2D matrix arrays for 3D ultrasound imaging is very challenging in terms of cable size, wiring and data rate. The sparse array approach tackles this problem by optimally distributing a reduced number of elements over a 2D aperture while preserving a decent image quality and beam steering capabilities. Unfortunately, reducing the number of elements significantly reduces the active probe footprint reducing as a consequence the sensitivity and at the end the signal-to-noise ratio. Here we propose a new coded excitation scheme based on complete complementary codes to increase the signal-to-noise ratio in 3D ultrasound imaging with sparse arrays. These codes are known for their ideal auto-correlation and cross-correlation properties and have been widely used in Code-Division Multiple Access systems (CDMA). An algorithm for generating such codes is presented as well as the adopted imaging sequence. The proposed method has been compared in simulations to other coded excitation schemes and showed significant increase in the signal-to-noise ratio of sparse arrays with no correlation artifacts and no frame rate reduction. The gain in signal-to-noise ratio compared to the case where no coded excitation is used was around [Formula: see text] and the contrast was also improved by [Formula: see text] while the resolution was unchanged.

Continuous Emission Ultrasound: A New Paradigm to Ultrafast Ultrasound Imaging.

Current imaging techniques in echography rely on the pulse-echo (PE) paradigm which provides a straight-forward access to the in-depth structure of tissues. They inherently face two major challenges: the limitation of the pulse repetition frequency, directly linked to the imaging framerate, and, due to the emission scheme, their blindness to the phenomena that happen in the medium during the majority of the acquisition time. To overcome these limitations, we propose a new paradigm for ultrasound imaging, denoted by continuous emission ultrasound imaging (CEUI) [1], for a single input single output (SISO) device. A continuous insonification of the medium is done by the probe using a coded waveform inspired from the radar and sonar literature. A framework coupling a sliding window approach (SWA) and pulse compression methods processes the recorded echoes to rebuild a motion-mode (M-mode) image from the medium with a high temporal resolution compared to state-of-the-art ultrafast imaging methods. A study on realistic simulated data, with regards to the motion of the medium, has been carried out and, achieved results assess an unequivocal improvement of the slow time frequency up to, at least, two orders of magnitude compared to ultrafast US imaging methods. This enhancement leads, therefore, to a ten times improvement in the temporal separability of the imaging system. In addition, it demonstrates the capability of CEUI to catch relatively short and quick events, in comparison to the imaging period of PE methods, at any instant of the acquisition.

Liner orientation change of dual mobility cup determined via 3D ultrasound imaging and motion analysis: A cadaver study.

BACKGROUND: A mobile polyethylene liner enables the dual mobility cup (DMC) to contribute to restoring hip joint range-of-motion, decreasing wear and increasing implant stability. However, more data is required on how liner orientation changes with hip joint movement. As a first step towards better understanding liner orientation change in vivo, this cadaver study focuses on quantifying DMC liner orientation change after different hip passive movements, using ultrasound imaging and motion analysis. HYPOTHESIS: The liner does not always go back to its initial orientation and its final orientation depends mainly on hip movement amplitude. METHODS: 3D ultrasound imaging and motion analysis were used to define liner and hip movements for four fresh post-mortem human subjects with six implanted DMC. Abduction and anteversion angles of the liner plane relative to the pelvis were measured before and after hip flexion, internal rotation, external rotation, abduction, adduction. RESULTS: Liner orientation changes were generally defined by angle variation smaller than 5°, with the liner nearly going back to its initial orientation. However, hip flexion caused liner abduction and anteversion angle variations greater than 15°. Except for hip adduction, only weak or no correlation was found between the final angle of the liner and the maximal hip joint movement amplitude. DISCUSSION: This study is the first attempt to quantify liner orientation change for implanted DMC via ultrasound imaging and constitutes a step forward in the understanding of liner orientation change and its relationship with hip joint movement. The hypothesis that the final liner abduction and anteversion angles depend mainly on hip movement amplitude was not confirmed, even if hip flexion was the movement generating the most liner orientation changes over 15°. This approach should be extended to in vivo clinical investigations, as measured liner angle variation could provide important support for the wear and stability claims made for DMC. LEVEL OF EVIDENCE: IV; cadaveric study.

Automatic needle detection and tracking in 3D ultrasound using an ROI-based RANSAC and Kalman method.

This article proposes a robust technique for needle detection and tracking using three-dimensional ultrasound (3D US). It is difficult for radiologists to detect and follow the position of micro tools, such as biopsy needles, that are inserted in human tissues under 3D US guidance. To overcome this difficulty, we propose a method that automatically reduces the processed volume to a limited region of interest (ROI), increasing at the same time the calculation speed and the robustness of the proposed technique. First, a line filter method that enhances the contrast of the needle against the background is used to facilitate the initialization of ROI using the tubularness information of the complete US volume. Then, the random sample consensus (RANSAC) and Kalman filter (RK) algorithm is used in the ROI to detect and track the precise position of the needle. A series of numerical inhomogeneous phantoms with a needle simulated from real 3D US volumes are used to evaluate our method. The results show that the proposed method is much more robust than the RANSAC algorithm when detecting the needle, regardless of whether or not the insertion axis corresponds to an acquisition plane in the 3D US volume. The possibility of failure is also discussed in this article.

Optimized Virtual Sources Distributions for 3-D Ultrafast Diverging Wave Compounding Imaging: A Simulation Study.

Ultrafast ultrasound imaging allows observing rapid phenomena; combined with 3-D imaging it has the potential to provide a more accurate analysis of organs which leads, in the end, to better diagnosis. Coherent compounding using diverging waves is commonly used to reconstruct high-quality images on large volumes while keeping the frame rate high enough to allow dynamic analysis. In practice, the virtual sources (VSs) that drive the diverging waves are often distributed in a deterministic way: following a regular grid, concentric rings, and spirals. Even though those deterministic distributions can offer various tradeoffs in terms of imaging performance, other distributions can be considered to improve imaging performance. It is herein suggested to look at alternative VSs distributions for optimizing the lateral resolution and the secondary lobes level (SLL) on several point spread functions (PSFs) by means of a multiobjective genetic algorithm. The optimization framework has led to seven pseudo-irregular distributions of VSs distributions that have not yet been found in the literature. An analysis of the imaging performance with a simulated phantom shows that these new distributions offer different tradeoffs between lateral resolution and contrast, respectively, measured on point-like reflectors and anechoic cysts. As an example, one of these optimized distributions improves the lateral resolution by 16% and gives equivalent contrast values on cysts and PSF isotropy properties, when compared to a concentric-rings-based distribution.

Cancer characterization using light backscattering spectroscopy and quantitative ultrasound: an ex vivo study on sarcoma subtypes.

Histological analysis is the gold standard method for cancer diagnosis. However, it is prone to subjectivity and sampling bias. In response to these limitations, we introduce a quantitative bimodal approach that aims to provide non-invasive guidance towards suspicious regions. Light backscattering spectroscopy and quantitative ultrasound techniques were combined to characterize two different bone tumor types from animal models: chondrosarcomas and osteosarcomas. Two different cell lines were used to induce osteosarcoma growth. Histological analyses were conducted to serve as references. Three ultrasound parameters and intensities of the light reflectance profiles showed significant differences between chondrosarcomas and osteosarcomas at the 5% level. Likewise, variations in the same biomarkers were reported for the two types of osteosarcoma, despite their similar morphology observed in the histological examinations. These observations show the sensitivity of our techniques in probing fine tissue properties. Secondly, the ultrasound spectral-based technique identified the mean size of chondrosarcoma cells and nuclei with relative errors of about 22% and 9% respectively. The optical equivalent technique correctly extracted scatterer size distributions that encompass nuclei and cells for chondrosarcomas and osteosarcomas ([Formula: see text] and [Formula: see text] respectively). The optical scattering contributions of nuclei were estimated at 52% for the chondrosarcomas and 69% for the osteosarcomas, probably indicating the abundant and the absent extracellular matrix respectively. Thus, the ultrasound and the optical methods brought complementary parameters. They successfully estimated morphological parameters at the cellular and the nuclear scales, making our bimodal technique promising for tumor characterization.

Design, Implementation, and Medical Applications of 2-D Ultrasound Sparse Arrays.

An ultrasound sparse array consists of a sparse distribution of elements over a 2-D aperture. Such an array is typically characterized by a limited number of elements, which in most cases is compatible with the channel number of the available scanners. Sparse arrays represent an attractive alternative to full 2-D arrays that may require the control of thousands of elements through expensive application-specific integrated circuits (ASICs). However, their massive use is hindered by two main drawbacks: the possible beam profile deterioration, which may worsen the image contrast, and the limited signal-to-noise ratio (SNR), which may result too low for some applications. This article reviews the work done for three decades on 2-D ultrasound sparse arrays for medical applications. First, random, optimized, and deterministic design methods are reviewed together with their main influencing factors. Then, experimental 2-D sparse array implementations based on piezoelectric and capacitive micromachined ultrasonic transducer (CMUT) technologies are presented. Sample applications to 3-D (Doppler) imaging, super-resolution imaging, photo-acoustic imaging, and therapy are reported. The final sections discuss the main shortcomings associated with the use of sparse arrays, the related countermeasures, and the next steps envisaged in the development of innovative arrays.

Prognostic significance of vascular and valvular calcifications in low- and high-gradient aortic stenosis.

AIMS: In low-gradient aortic stenosis (LGAS), the high valvulo-arterial impedance observed despite low valvular gradient suggests a high vascular load. Thoracic aortic calcifications (TACs) and valvular aortic calcifications (VACs) are, respectively, surrogates of aortic load and aortic valvular gradient. The aim of this study was to compare the respective contributions of TAC and VAC on 3-year cardiovascular (CV) mortality following TAVI in LGAS vs. high-gradient aortic stenosis (HGAS) patients. METHODS AND RESULTS: A total of 1396 consecutive patients were included. TAC and VAC were measured on the pre-TAVI CT-scan. About 435 (31.2%) patients had LGAS and 961 (68.8%) HGAS. LGAS patients were more prone to have diabetes, coronary artery disease (CAD), atrial fibrillation (AF), and lower left ventricular ejection fraction (LVEF), P<0.05 for all. During the 3 years after TAVI, 245(17.8%) patients experienced CV mortality, 92(21.6%) in LGAS and 153(16.2%) in HGAS patients, P=0.018. Multivariate analysis adjusted for age, gender, diabetes, AF, CAD, LVEF, renal function, vascular access, and aortic regurgitation showed that TAC but not VAC was associated with CV mortality in LGAS, hazard ratio (HR) 1.085 confidence interval (CI) (1.019-1.156), P=0.011, and HR 0.713 CI (0.439-1.8), P=0.235; the opposite was observed in HGAS patients with VAC but not TAC being associated with CV mortality, HR 1.342 CI (1.034-1.742), P=0.027, and HR 1.015 CI (0.955-1.079), P=0.626. CONCLUSION: TAC plays a major prognostic role in LGAS while VAC remains the key in HGAS patients. This confirms that LGAS is a complex vascular and valvular disease.

Accuracy and precision of the measurement of liner orientation of dual mobility cup total hip arthroplasty using ultrasound imaging.

The Dual Mobility Cup (DMC) was created in 1974 to prevent dislocation and decrease wear. However, the movement of the polyethylene liner in vivo remains unclear. The aims of this study were to visualise liner positions and quantify the accuracy of the liner plane orientation for static positions, using ultrasound imaging. DMC reconstruction and angle between cup and liner were evaluated on isolated submerged DMCs by comparing 3D laser scans and ultrasound imaging. Moreover, the abduction and anteversion angles of the liner plane relative to the pelvis orientation were calculated via combined motion analysis and 3D ultrasound imaging on four fresh post-mortem human subjects with implanted DMC. On submerged DMC, the mean angle error between ultrasound imaging and 3D scan was 1.2°. In cadaveric experiments, intra-operator repeatability proved satisfactory, with low range value (lower than 2°) and standard deviation (lower than 1°). The study demonstrates the feasibility of measuring liner orientation on submerged and ex vivo experiments using ultrasound imaging, and is a first step towards in vivo analysis of DMC movement.

Carotid Ultrasound Boundary Study (CUBS): Technical considerations on an open multi-center analysis of computerized measurement systems for intima-media thickness measurement on common carotid artery longitudinal B-mode ultrasound scans.

After publishing an in-depth study that analyzed the ability of computerized methods to assist or replace human experts in obtaining carotid intima-media thickness (CIMT) measurements leading to correct therapeutic decisions, here the same consortium joined to present technical outlooks on computerized CIMT measurement systems and provide considerations for the community regarding the development and comparison of these methods, including considerations to encourage the standardization of computerized CIMT measurements and results presentation. A multi-center database of 500 images was collected, upon which three manual segmentations and seven computerized methods were employed to measure the CIMT, including traditional methods based on dynamic programming, deformable models, the first order absolute moment, anisotropic Gaussian derivative filters and deep learning-based image processing approaches based on U-Net convolutional neural networks. An inter- and intra-analyst variability analysis was conducted and segmentation results were analyzed by dividing the database based on carotid morphology, image signal-to-noise ratio, and research center. The computerized methods obtained CIMT absolute bias results that were comparable with studies in literature and they generally were similar and often better than the observed inter- and intra-analyst variability. Several computerized methods showed promising segmentation results, including one deep learning method (CIMT absolute bias = 106 ± 89 µm vs. 160 ± 140 µm intra-analyst variability) and three other traditional image processing methods (CIMT absolute bias = 139 ± 119 µm, 143 ± 118 µm and 139 ± 136 µm). The entire database used has been made publicly available for the community to facilitate future studies and to encourage an open comparison and technical analysis (https://doi.org/10.17632/m7ndn58sv6.1).

Sparse Convolutional Beamforming for 3-D Ultrafast Ultrasound Imaging.

Real-time 3-D ultrasound (US) provides a complete visualization of inner body organs and blood vasculature, crucial for diagnosis and treatment of diverse diseases. However, 3-D systems require massive hardware due to the huge number of transducer elements and consequent data size. This increases cost significantly and limit both frame rate and image quality, thus preventing the 3-D US from being common practice in clinics worldwide. A recent study presented a technique called sparse convolutional beamforming algorithm (SCOBA), which obtains improved image quality while allowing notable element reduction in the context of 2-D focused imaging. In this article, we build upon previous work and introduce a nonlinear beamformer for 3-D imaging, called COBA-3D, consisting of 2-D spatial convolution of the in-phase and quadrature received signals. The proposed technique considers diverging-wave transmission and achieves improved image resolution and contrast compared with standard delay-and-sum beamforming while enabling a high frame rate. Incorporating 2-D sparse arrays into our method creates SCOBA-3D: a sparse beamformer that offers significant element reduction and, thus, allows performing 3-D imaging with the resources typically available for 2-D setups. To create 2-D thinned arrays, we present a scalable and systematic way to design 2-D fractal sparse arrays. The proposed framework paves the way for affordable ultrafast US devices that perform high-quality 3-D imaging, as demonstrated using phantom and ex-vivo data.

Tapered Vector Doppler for Improved Quantification of Low Velocity Blood Flow.

A new vector velocity estimation scheme is developed, termed tapered vector Doppler (TVD), aiming to improve the accuracy of low velocity flow estimation. This is done by assessing the effects of singular value decomposition (SVD) and finite impulse response (FIR) filters and designing an estimator which accounts for signal loss due to filtering. Synthetic data created using a combination of in vivo recordings and flow simulations were used to investigate scenarios with low blood flow, in combination with true clutter motion. Using this approach, the accuracy and precision of TVD was investigated for a range of clutter-to-blood and signal-to-noise ratios. The results indicated that for the investigated carotid application and setup, the SVD filter performed as a frequency-based filter. For both SVD and FIR filters, suppression of the clutter signal resulted in large bias and variance in the estimated blood velocity magnitude and direction close to the vessel walls. Application of the proposed tapering technique yielded significant improvement in the accuracy and precision of near-wall vector velocity measurements, compared to non-TVD and weighted least squares approaches. In synthetic data, for a blood SNR of 5 dB, and in a near-wall region where the average blood velocity was 9 cm/s, the use of tapering reduced the average velocity magnitude bias from 26.3 to 1.4 cm/s. Complex flow in a carotid bifurcation was used to demonstrate the in vivo performance of TVD, and it was shown that tapering enables vector velocity estimation less affected by clutter and clutter filtering than what could be obtained by adaptive filter design only.

Real-Time 3-D Spectral Doppler Analysis With a Sparse Spiral Array.

2-D sparse arrays may push the development of low-cost 3-D systems, not needing to control thousands of elements by expensive application-specific integrated circuits (ASICs). However, there is still some concern about their suitability in applications, such as Doppler investigation, which inherently involve poor signal-to-noise ratios (SNRs). In this article, a novel real-time 3-D pulsed-wave (PW) Doppler system, based on a 256-element 2-D spiral array, is presented. Coded transmission (TX) and matched filtering were implemented to improve the system SNR. Standard sonograms as well as multigate spectral Doppler (MSD) profiles, along lines that can be arbitrarily located in different planes, are presented. The performance of the system was assessed quantitatively on experimental data obtained from a straight tube flow phantom. An SNR increase of 11.4 dB was measured by transmitting linear chirps instead of standard sinusoidal bursts. For a qualitative assessment of the system performance in more realistic conditions, an anthropomorphic phantom of the carotid arteries was used. Finally, real-time B-mode and MSD images were obtained from healthy volunteers.

Translation of Simultaneous Vessel Wall Motion and Vectorial Blood Flow Imaging in Healthy and Diseased Carotids to the Clinic: A Pilot Study.

This study aims to investigate the clinical feasibility of simultaneous extraction of vessel wall motion and vectorial blood flow at high frame rates for both extraction of clinical markers and visual inspection. If available in the clinic, such a technique would allow a better estimation of plaque vulnerability and improved evaluation of the overall arterial health of patients. In this study, both healthy volunteers and patients were recruited and scanned using a planewave acquisition scheme that provided a data set of 43 carotid recordings in total. The vessel wall motion was extracted based on the complex autocorrelation of the signals received, while the vector flow was extracted using the transverse oscillation technique. Wall motion and vector flow were extracted at high frame rates, which allowed for a visual appreciation of tissue movement and blood flow simultaneously. Several clinical markers were extracted, and visual inspections of the wall motion and flow were conducted. From all the potential markers, young healthy volunteers had smaller artery diameter (7.72 mm) compared with diseased patients (9.56 mm) ( p -value ≤ 0.001), 66% of diseased patients had backflow compared with less than 10% for the other patients ( p -value ≤ 0.05), a carotid with a pulse wave velocity extracted from the wall velocity greater than 7 m/s was always a diseased vessel, and the peak wall shear rate decreased as the risk increases. Based on both the pathological markers and the visual inspection of tissue motion and vector flow, we conclude that the clinical feasibility of this approach is demonstrated. Larger and more disease-specific studies using such an approach will lead to better understanding and evaluation of vessels, which can translate to future use in the clinic.

Spectral Doppler Measurements With 2-D Sparse Arrays.

The 2-D sparse arrays, in which a few hundreds of elements are distributed on the probe surface according to an optimization procedure, represent an alternative to full 2-D arrays, including thousands of elements usually organized in a grid. Sparse arrays have already been used in B-mode imaging tests, but their application to Doppler investigations has not been reported yet. Since the sparsity of the elements influences the acoustic field, a corresponding influence on the mean frequency (Fm), bandwidth (BW), and signal-to-noise ratio (SNR) of the Doppler spectra is expected. This article aims to assess, by simulations and experiments, to what extent the use of a sparse rather than a full gridded 2-D array has an impact on spectral Doppler measurements. Parabolic flows were investigated by a 3 MHz, 1024-element gridded array and by a sparse array; the latter was obtained by properly selecting a subgroup of 256 elements from the full array. Simulations show that the mean Doppler frequency does not change between the sparse and the full array while there are significant differences on the BW (average reduction of 17.2% for the sparse array, due to different apertures of the two probes) and on the signal power (Ps) (22 dB, due to the different number of active elements). These results are confirmed by flow phantom experiments, which also highlight that the most critical difference between sparse and full gridded array in Doppler measurements is in terms of SNR (-16.8 dB).

Investigation of PVA cryogel Young's modulus stability with time, controlled by a simple reliable technique.

We describe a quasistatic method for mechanical characterization of tissue-mimicking material used in elastography. We demonstrate that it is possible to assess the elasticity modulus with a reasonable reproducibility using simple and easy tools and methods. Possessing a simple relevant technique with evaluated relative error to assess Young's modulus of these phantoms could deeply improve the quality of the research in the field of elastography. The method was tested and validated with four samples of polyvinyl alcohol (PVA) cryogel with different elasticity values corresponding to those of stiffer soft biological tissues. Young's moduli, varying from 70 to 180 kPa depending on the number of freeze-thaw cycles (two to five), were measured within strict measurement conditions and found to have a reproducibility varying from 4% to 8%. Relative error, estimated as the ratio between observed and reference values, varied from 16% to 32%. Besides, measurement stability over 4 months was evaluated. The method demonstrated good feasibility and acceptable reproducibility for mechanically characterizing and controlled over time phantoms used for validating new potential ultrasound imaging techniques in the field of elastography. Nevertheless, in this study, investigation was performed on gel possessing young's modulus values ranging from 80 to 215 kPa. Some tissue values of Young'modulus were reported to be lower, ranging from 0.6 to 28 kPa as liver or glandular values. Consequently, further validation of this static method for mechanical characterization of phantom gels should be performed using softer PVA cryogel.

Analytic estimation of subsample spatial shift using the phases of multidimensional analytic signals.

In this correspondence, a method of analytic subsample spatial shift estimation based on an a priori n-D signal model is proposed. The estimation uses the linear phases of n analytic signals defined with the multidimensional Hilbert transform. This estimation proposes: i) an analytic solution to the n-D shift estimation and ii) an estimation without processing complex cross-correlation function or cross-spectra between signals contrary to most phase shift estimators. The method provides better performance in estimating subsample shifts than two classical estimators, one using the maximum of cross-correlation function and the other seeking the zero of the complex correlation function phase. Two delay estimators using the in-phase and quadrature-phase components of signals are also compared to our estimator. Like most estimators using the complex signal phases, the estimator proposed herein presents the advantage of unaltered accuracy when low sampled signals are used. Moreover, we show that this method can be applied to motion tracking with ultrasound images. Thus, included in a block-based motion estimation method and tested with ultrasound data, this estimator provides an analytical solution to the translation estimation problem.