Sign-Coherence-Factor-Based Suppression for Grating Lobes in Through-Wall Radar Imaging

In recent years, many research studies have been carried out on ultrasound computed tomography (USCT) for its application prospect in early diagnosis of breast cancer. This paper applies four kinds of coherence-factor-like beamforming methods to improve the image quality of synthetic aperture focusing method for USCT, including the coherence-factor (CF), the phase coherence factor (PCF), the sign coherence factor (SCF) and the spatial smoothing coherence factor (SSCF) (proposed in our previous work). The performance of these methods was tested with simulated raw data which were generated by the ultrasound simulation software PZFlex 2014. The simulated phantom was set to be water of 4cm diameter with three nylon objects of different diameters inside. The ring-type transducer had 72 elements with a center frequency of 1MHz. The results show that all the methods can reveal the biggest nylon circle with the radius of 2.5mm. SSCF gets the highest SNR among the proposed methods and provides a more homogenous background. None of these methods can reveal the two smaller nylon circles with the radius of 0.75mm and 0.25mm. This may be due to the small number of elements.

A new method for grating and side lobes suppression in ultrasound images is presented. It is based on an analysis of the phase diversity at the aperture data. Two coherence factors, namely the phase coherence factor (PCF) and the sign coherence factor (SCF), are proposed to weight the coherent sum output. Different from other approaches, phase rather than amplitude information is used to perform the correction action. Besides achieving the main goal, the method obtains improvements in lateral resolution and SNR. Implementation of the SCF technique is quite straightforward, operating in realtime, and can be added to any virtually existing beamformer to improve the resolution, contrast, SNR, and dynamic range of the images. A programmable parameter allows adjusting the sensitivity of the method to out-of-phase signals, from zero to a strict coherence criterion. The theoretical basis for the 2 methods are given and their performances evaluated by simulation. Then, experiments are conducted to provide results that are in good agreement with those expected from theory and simulation.

This paper presents a technique for improving the internal imaging of a solid object immersed in water using an ultrasonic array. This technique consists in determining the position and shape of a convex object surface using a combination of synthetic transmit aperture (STA) and sign coherence factor (SCF) methods. The SCF attenuates the grating lobe noise. The technique is applied to a cylindrical aluminium object with internal holes simulating defects. The first step is the acquisition of a sequence of STA images with SCF, using a distinct group of adjacent array elements for each image. In the second step, a circle is fitted to the positions of the peak values in each image. Finally, using the Fermat's principle and this circle as the interface between the water and the metallic object, the propagation delays from the array elements to the image grid points may be calculated and used in another STA image. In this final image, the small holes in the cylindrical object can clearly be identified. The effects of the SCF for a large diameter circular reflector are simulated and compared with experimental data.

A method combining Green's function retrieval theory and sign coherence factor (SCF) imaging is presented to detect near-surface defects in rails. The defects are close to the ultrasonic phased array and near-surface acoustic information of defects is obscured by the non-linear effects of the initial wave signal in directly acquired responses. To overcome this problem, cross-correlations of the diffuse field signals captured by the array transducer are performed to reconstruct the Green's function. SCF imaging is used to further improve the spatial resolution and signal-to-noise ratio (SNR) of near-surface defects in rails. Experiments are conducted on two rails containing two and four defects, respectively. The results show that these defects can be clearly identified when using the reconstructed Green's function. However, the images of near-surface defects are masked and cannot be distinguished when using directly captured signals and total focus imaging. The proposed method reduces the background noise and allows for effective imaging of near-surface defects in rails.

BACKGROUND: The coherent plane wave compounding (CPWC) is a promising technique to enhance the imaging quality while maintaining the high frame rate in the plane wave ultrasound imaging. Recently, the spatial-coherence-based method has been specially designed to process echo matrix required by the minimum variance (MV) method.OBJECTIVE: In this paper, a novel beamforming method that integrates the submatrix-spatial-coherence-based MV with the sign coherence factor (SCF) is proposed to further improve the imaging quality.METHOD: The submatrix smoothing technique is modified to smooth and de-correlate signals of the receiving array dimension. Then, the SCF is used to modify the input vector of the beamformer, which can reduce side lobe noises with almost no increase in the amount of calculation. Simulation, phantom, in vivo, and sound velocity error experiments have been performed to verify the superiority of the proposed beamformer.RESULTS: The imaging results show that the proposed approach performs better in the imaging resolution and contrast compared to the traditional CPWC method.CONCLUSION: The robustness of the proposed method is enhanced, and the over-suppression phenomenon can be alleviated, which is a phenomenon that occurs in the original spatial-coherence and SCF methods.

Improved Coherent Plane-Wave Compounding Using Sign Coherence Factor Weighting for Frequency-Domain Beamforming.

Integrating the ultrasonic pulse-echo (PE) and optoacousic (OA) imaging is a potent approach in rendering the volumetric images of biological tissues. The deliverable information are essentially uncorrelated but highly complementary in learning about the optical and mechanical properties of the medium. Yet, owing to the inhomogeneities in acoustic velocity and the optical scattering, this synergistic approach suffers from the low depth resolution, low contrast and artifacts like off-axis contributions and phase distortion. In this work, an adaptive weighted dynamic focusing based reconstruction technique namely, weighted synthetic aperture (WSA), has been developed to address the aforementioned defects, in particular for annular array. Our findings show the efficiency of WSA method in 3D reconstruction of simulated phantom. We elaborate WSA to estimate the spatial location, size, reflectivity function and absorption coefficient of the insonified/illuminated targets for both imaging modalities. The phase distortion introduced by the separable delay approximation is addressed with an adaptive weighting factor that combines coherence factor (CF) and phase coherence factor (PCF). In addition, the weighting factor incorporates the spatial impulse response (SIR), which is associated with the properties of the transducer in order to inverse the effect of the transducer on imaging quality. Using numerical phantom, the simulation results demonstrate that incorporating SIR into the weighting factor ensures the isotropic sensitivity while CF and PCF are suppressing the artifacts, grating lobe and phase aberration for both OA and PE images.

Damage localization in aluminum plate with compact rectangular phased piezoelectric transducer array

Most works that address 2-D array ultrasonic transducers for underwater applications are about the geometry aspects of the array and beamforming techniques to make 3-D images. They look for techniques to reduce the number of elements from wide apertures, maintaining the side lobes and the grating lobes at acceptable levels, but not many details about the materials and fabrication processes are described. To overcome these gaps, this paper presents in detail the development of a 2-D array ultrasonic transducer prototype that can individually emit and receive ultrasonic pulses to make 3-D images of immersed reflectors within a volume of interest (VOI). It consists of a 4 × 4 matrix ultrasonic transducer with a central frequency of 480 kHz. Each element is a 5 mm sided square cut into a 1–3 piezocomposite. The center-to-center distance of two contiguous elements (pitch) was chosen to be greater than half wavelength, to increase the amplitude of emission and reception of signals with larger elements. Artifacts generated by grating lobes were avoided by restricting the field of view in the azimuth and elevation directions within 40° × 40° and applying the sign coherence factor (SCF) filter. Two types of backing layer materials were tested, one with air and another made of epoxy resin, on the transducers called T1 and T2, respectively. The pulse echoes measured with T1 had 2.6 dB higher amplitude than those measured with T2, and the bandwidths were 54% and 50% @ −6 dB, respectively, exciting the element with a single rectangular negative pulse. The 3-D images obtained with full matrix capture (FMC) data sets acquired of objects from 0.2 to 1.15 m motivate the development of a 2-D array transducer with more elements, to increase the angular resolution and the range.

Ultrafast ultrasound imaging allows total focusing on every pixel, but it uses a non-focusing transmission of the ultrasonic wave into the tissue. Based on plane wave or diverging wave imaging, additional clutter reduces the imaging quality especially in echo-free regions like cysts. Clutter reducing techniques like adaptive beamforming processing compute weighting factors based on measured channel data used for each sample reconstruction. This increases signal and image quality again but adds computational complexity and may result in techniques that are not real-time capable to be implemented in an ultrasound scanner. A fast and accurate phase estimator for real-time applications is needed. Extending the concept of sign coherence factor (SCF) computations using bi-phase estimations, we propose a fast quad phase coherence (QPC) estimator for more accurate phase detection to reduce incoherent clutter. Instead of only using the sign coherence of each of the single channel data, the QPC estimator also includes the monotony of the signal to differentiate into the four classes “positive sign & increasing monotony”, “positive sign & decreasing monotony ”, “negative sign & decreasing monotony” and “negative sign & increasing monotony”. The dominant class of these four is selected and the adaptive weighting is computed as ratio of the absolute frequency of this class to the sum of all other class occurrences. The calculation of the monotony introduces only a small computational overhead compared to other adaptive beamforming techniques. The performance of QPC usage is evaluated using our ultrafast ultrasound research systems at phantom measurements (using “DiPhAS” system with 128 parallel channels) and in-vivo bladder measurements (using “MoUsE” system with 32 parallel channels, 3 MHz phased array transducer). The beamforming reconstruction is computed on the performance-limited integrated PC hardware as OpenCL kernel in real time. Imaging performance is increased compared to sign coherence beamforming (SNR by >3 dB, contrast by 4,4 dB, spatial resolution PSF FWHM by 19 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</sup> ) while computation time still allows real-time usage.

In recent years, ultrasound has been increasingly used to guide needle insertion procedures for spinal anesthesia. The primary anatomical targets are facet joints and epidural spaces. For these procedures, accurate visualization of the spine anatomy is of critical importance. Challenges arising from the interactions between the ultrasound beam and spinal structures including tilt caused by specular reflections, off-axis interference, and reverberations often result in weakened and blurred vertebra surfaces. Previously, adaptive beamforming methods have been proposed to improve the resolution and contrast. However, most of these methods are not specialized for improving the contrast of specular targets like bones. In this paper, we propose an accumulated angle factor (AAF)-based beamforming method customized for bone surface enhancement. This approach applies a Hilbert transform on delay compensated channel data across the receive aperture. The accumulated phase change across the receive aperture is then calculated and utilized as the weight in the beamforming output. We compared our method with classical delay and sum (DAS) beamforming method and adaptive beamforming methods such as Wiener, phase coherence factor (PCF), CF, and generalized CF (GCF) beamforming. In 12 volunteer data sets, the mean contrast ratio between the vertebrae surface and the surrounding tissue for DAS, Wiener, PCF, CF, GCF, and the proposed AAF methods are 0.49, 0.64, 0.82, 0.77, 0.76, and 0.91, respectively. The contrast is significantly improved in the proposed method.

Various methods have been proposed to estimate the tissue speed of sound (SOS) of propagating medium using the curvature of received channel waveform or the analysis of resultant image quality. In our previous study, baseband delay-multiply-and-sum (DMAS) beamforming methods have been developed for multi-angle plane-wave (PW) imaging which relies on signal coherence among transmit events (Tx-DMAS) or receive channel (Rx-DMAS) or both (2D-DMAS) to suppress low-coherence clutters. In this study, we further extend our DMAS beamforming to quantify the level of signal coherence for determining the average SOS in multi-angle PW imaging. The signal coherence in multi-angle PW imaging is represented as the phase coherence factor (PCF) which can be easily estimated from the magnitude ratio of the pixel value of DMAS image to that of DAS image. By searching the beamforming velocity that provides the highest signal coherence of echo matrix, the averaged tissue SOS of the image object can be determined. For the PICMUS experimental dataset, the optimal beamforming velocity $(C_{opt})$ estimated by the proposed PCF method does provide the best image quality. For the Prodigy dataset, the estimated tissue SOS is 1426±6 m/s which is very close to the actual tissue SOS of 1427 m/s and the estimated SOS also corresponds to the $C_{opt}$ with the minimal −6-dB LW and the maximal CR within an error of 10 m/s.

In recent years, several attempts have been made in designing planar array antennas with high directivity. This paper is aimed at investigating the impact of element spacing on the directivity of planar array of monopole antenna. The directivity of antenna with reduced grating lobes can be obtained by carefully varying the inter-element spacing of array antenna. Based on this conception, this paper presents the investigation carried out on the relationship between inter-element spacing and the directivity of planar array of monopole antenna. It went further to highlight the effect on the total fields radiated by the antenna. The inter-element spacing is one of the most important antenna parameters that determine the directivity of the antenna. For a planar array of monopole, the directivity can be improved by varying the inter-element spacing. Four elements uniform planar array antenna and Hadamard matrix method was used to determine element positioning in the array matrix. The simulated results obtained using Matlab, showed that good directivity was obtained by using element spacing between 0.1λ - 0.5λ. Increasing the spacing beyond 0.6λ - 1.0λ also improved the directivity, but generated many grating lobes. As inter-element spacing increased, the grating lobes increased in size, number and levels. The study, therefore, inferred that the best directivity (radiation pattern) can only be obtained when the element spacing is within 0.1 - 0.5λ.

A high-gain ridge gap array antenna, consists of an array of 2×8 monopole antennas with inter-element spacing equals to a wavelength, is proposed and investigated as a promising state-of-the-art grating lobe suppressed high-gain array for millimeter-wave frequency-bands. Increasing the inter-element spacing is a technique for enhancing the directivity; however, it would bring the grating lobe into the visible zone and deteriorate the antenna radiation efficiency. The proposed technique using a supplementary sub-array would suppress the grating lobe in the visible zone. On the other hand, the feeding network is designed with ridge gap waveguide technology in which the waveguide width is about a wavelength making the design of an array antenna with lower inter-element spacing more challenging.

The Montgomery Ladder is widely used for implementing the scalar multiplication in elliptic curve cryptographic designs. This algorithm is efficient and provides a natural robustness against (simple) side-channel attacks. Previous works however showed that implementations of the Montgomery Ladder using Lopez-Dahab projective coordinates easily leak the value of the most significant bits of the secret scalar, which led to a full key recovery in an attack known as LadderLeak [3]. In light of such leakage, we analyse further popular methods for implementing the Montgomery Ladder. We first consider open source software implementations of the X25519 protocol which implement the Montgomery Ladder based on the ladderstep algorithm from Düll et al. [15]. We confirm via power measurements that these implementations also easily leak the most significant scalar bits, even when implementing Z-coordinate randomisations. We thus propose simple modifications of the algorithm and its handling of the most significant bits and show the effectiveness of our modifications via experimental results. Particularly, our re-designs of the algorithm do not incurring significant efficiency penalties. As a second case study, we consider open source hardware implementations of the Montgomery Ladder based on the complete addition formulas for prime order elliptic curves, where we observe the exact same leakage. As we explain, the most significant bits in implementations of the complete addition formulas can be protected in an analogous way as we do for Curve25519 in our first case study.KeywordsECCMontgomery LadderCurve25519Complete addition formulasSide-channel analysis