Sparse Array Imaging Research Articles

Optimization of Sparse Camera Array Arrangement using Grid-based Method

—This study explores the application of multi-camera array technology in super-resolution (SR) imaging system. We propose an innovative method based on grid representation to optimize camera arrangements using sparse Gaussian processes and variational inference. This approach significantly enhances the image reconstruction quality of sparse camera arrays. Unlike conventional techniques that provide only qualitative conclusions, our grid-based method precisely optimizes camera positions and effectively simulates the impact of assembly errors. The optimized camera arrangement substantially improves the SR reconstruction quality of sparse array imaging systems, reducing contour jaggedness and high-frequency aliasing. Extensive simulations and experimental validations confirm the robustness and practical applicability of our method. The results demonstrate that the optimized camera arrangements can achieve high-resolution imaging with enhanced robustness against assembly errors, indicating their potential for various applications such as biological microscopy, remote sensing, and smartphone photography. This work presents a new and effective strategy for designing sparse camera array imaging systems, offering significant improvements in both image quality and system reliability.

Deep learning assisted sparse array ultrasound imaging.

This study aims to restore grating lobe artifacts and improve the image resolution of sparse array ultrasonography via a deep learning predictive model. A deep learning assisted sparse array was developed using only 64 or 16 channels out of the 128 channels in which the pitch is two or eight times the original array. The deep learning assisted sparse array imaging system was demonstrated on ex vivo porcine teeth. 64- and 16-channel sparse array images were used as the input and corresponding 128-channel dense array images were used as the ground truth. The structural similarity index measure, mean squared error, and peak signal-to-noise ratio of predicted images improved significantly (p < 0.0001). The resolution of predicted images presented close values to ground truth images (0.18 mm and 0.15 mm versus 0.15 mm). The gingival thickness measurement showed a high level of agreement between the predicted sparse array images and the ground truth images, as indicated with a bias of -0.01 mm and 0.02 mm for the 64- and 16-channel predicted images, respectively, and a Pearson's r = 0.99 (p < 0.0001) for both. The gingival thickness bias measured by deep learning assisted sparse array imaging and clinical probing needle was found to be <0.05 mm. Additionally, the deep learning model showed capability of generalization. To conclude, the deep learning assisted sparse array can reconstruct high-resolution ultrasound image using only 16 channels of 128 channels. The deep learning model performed generalization capability for the 64-channel array, while the 16-channel array generalization would require further optimization.

Sparse array radar forward-looking imaging based on fast atomic norm minimization

ABSTRACT The sparse array imaging radar could largely reduce the system complexity, but it also suffers from poor azimuthal resolution due to the limited aperture length and incomplete observation caused by non-uniform array configuration. In this letter, a radar forward-looking imaging method with improved imaging quality and reduced system complexity is proposed. Firstly, the matrix completion method is utilized to recover the missing signals of sparse array. Then, based on the plane-wave assumption, a fast 2-dimensional atomic norm minimization (ANM) is adopted to solve the positions and amplitudes of scatterers. As a continues compressed sensing method, the result of ANM-based method earns sharper main-lobes and much lower-level side-lobes compared to the fast Fourier transform -based method. Although the resolution of proposed method is still limited by Rayleigh resolution, the imaging quality can be greatly improved by emphasizing main-lobes and avoiding the perturbation of side-lobes. Simulations and experiments are carried out to demonstrate the performance of the proposed method.

Anisotropy influence on guided wave scattering for composite structure monitoring

Composite structures are widely used for aerospace applications but are prone to barely visible impact damage from low velocity impacts. Guided wave measurements using sparse arrays of distributed sensors provide an important structural health monitoring (SHM) tool for detecting and localizing impact damage in composites. However, the anisotropy of composites needs to be considered as it can affect guided wave propagation and scattering, impacting imaging performance. Improved defect characterization can be achieved by considering the scattering characteristics for the signal processing. Scattering around two different damage types for multiple incident wave directions in a quasi-isotropic carbon fiber reinforced polymer (CFRP) panel were investigated. Full 3D Finite Element (FE) simulations were compared to the measured scattered guided wave field at an artificial insert delamination. Permanent magnets mounted on an undamaged region of the plate were used as scattering targets and both numerical and experimental scattering patterns were compared to the delamination results. Strong directional dependency was observed for both damage types, with energy focusing along the fiber directions of the outer ply layers. For the delamination, mostly forward scattering is observed for all incident wave directions, whereas the magnet blocked forward wave transmission and scattered wave energy in all directions. 2D scattering matrices were calculated, demonstrating distinct scattering behavior for each damage type. Implications of anisotropy and angular scattering on SHM guided wave sparse array imaging are discussed.

Sparse 2-D PZT-on-PCB Arrays With Density Tapering.

Two-dimensional (2-D) arrays offer volumetric imaging capabilities without the need for probe translation or rotation. A sparse array with elements seeded in a tapering spiral pattern enables one-to-one connection to an ultrasound machine, thus allowing flexible transmission and reception strategies. To test the concept of sparse spiral array imaging, we have designed, realized, and characterized two prototype probes designed at 2.5-MHz low-frequency (LF) and 5-MHz high-frequency (HF) center frequencies. Both probes share the same electronic design, based on piezoelectric ceramics and rapid prototyping with printed circuit board substrates to wire the elements to external connectors. Different center frequencies were achieved by adjusting the piezoelectric layer thickness. The LF and HF prototype probes had 88% and 95% of working elements, producing peak pressures of 21 and 96 kPa/V when focused at 5 and 3 cm, respectively. The one-way -3-dB bandwidths were 26% and 32%. These results, together with experimental tests on tissue-mimicking phantoms, show that the probes are viable for volumetric imaging.

Real-Time Millimeter-Wave Imaging for Moving Targets Realized in a Sparse Array Based on InP-HBT MMICs

Millimeter-wave (MMW) imaging has been widely studied for applications, such as personnel screening and industrial noninvasive testing; however, real-time MMW imaging with a subcentimeter resolution and a large field of view (FoV) for a fast-moving target has been rarely reported to date. In this article, we present the design of such an imaging system at the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Ka$ </tex-math></inline-formula> -band utilizing the concept of multistatic sparse array. Microwave monolithic integrated circuits based on an InP-heterojunction bipolar transistor (HBT) technology are used for the transmitter and receiver chipsets. With the help of an improved backprojection algorithm and a computation platform based on field-programmable gate arrays, real-time imaging for a target moving as fast as about 10 m/s is demonstrated at a frame rate of over 20 frames/s. The imaging resolution is measured to be better than 6 mm and the FoV can reach over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\times 1\,\,\text{m}^{2}$ </tex-math></inline-formula> . Imaging of a moving person with concealed items is carried out to illustrate the system’s capability for personnel screening. To the best of the authors’ knowledge, this is the first real-time MMW sparse array imaging system built upon InP-HBT chipsets.

Near Field 3-D Millimeter-Wave SAR Image Enhancement and Detection with Application of Antenna Pattern Compensation

In this paper, a novel near-field high-resolution image focusing technique is proposed. With the emergence of Millimeter-wave (mmWave) devices, near-field synthetic aperture radar (SAR) imaging is widely used in automotive-mounted SAR imaging, UAV imaging, concealed threat detection, etc. Current research is mainly confined to the laboratory environment, thus ignoring the adverse effects of the non-ideal experimental environment on imaging and subsequent detection in real scenarios. To address this problem, we propose an optimized Back-Projection Algorithm (BPA) that considers the loss path of signal propagation among space by converting the amplitude factor in the echo model into a beam-weighting. The proposed algorithm is an image focusing algorithm for arbitrary and irregular arrays, and effectively mitigates sparse array imaging ghosts. We apply the 3DRIED dataset to construct image datasets for target detection, comparing the kappa coefficients of the proposed scheme with those obtained from classic BPA and Range Migration Algorithm (RMA) with amplitude loss compensation. The results show that the proposed algorithm attains a high-fidelity image reconstruction focus.

Advanced THz MIMO Sparse Imaging Scheme Using Multipass Synthetic Aperture Focusing and Low-Rank Matrix Completion Techniques

This article proposes an advanced THz multiple-input-multiple-output (MIMO) near-field sparse imaging scheme for target detection that uses single-pass synthetic aperture focusing and multipass interferometric synthetic aperture focusing techniques to improve imaging effectiveness and efficiency. It benefits from the MIMO of the linear sparse periodic array (SPA) and random undersampling sparse imaging to reduce sampling data and system cost. Both simulated and proof-of-concept experimental results have verified the scheme, revealing that the single-pass synthetic aperture imaging approach is sufficient to identify pure metallic targets with 3.87% of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda /2$ </tex-math></inline-formula> sampling data. The multipass interferometric synthetic aperture imaging approach is capable of improving image quality on the image signal-to-noise ratio (SNR) and contrast, which is ideal for detecting more challenging targets. The random sparse imaging with help of the low-rank matrix completion (LRMC) technique has shown the promising potential of achieving equivalent image quality when further reducing 43.75% data in the experiment of five-pass imaging on a complex target; this corresponds to 82.51% data reduction compared to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda /2$ </tex-math></inline-formula> sampling.

THz sparse periodic array imaging system using compressed sensing

This article studies the compressed sensing (CS) technique applied in the THz linear sparse periodic array (SPA) imaging system, proposing the corresponding image reconstruction model. The THz-SPA imaging system has been tested in electromagnetic (EM) simulation, and then experimentally verified by using a simplified set-up that only uses one transmitting channel and one receiving channel. The reconstructed images based on both simulation and experimental data have demonstrated the feasibility of CS reconstruction for reducing sampling data but maintaining comparable image quality as the traditional generalised synthetic aperture focusing technique.

Simultaneous excitation system for efficient guided wave structural health monitoring

Many structural health monitoring systems utilize guided wave transducer arrays for defect detection and localization. Signals are usually acquired using the “pitch-catch” method whereby each transducer is excited in turn and the response is received by the remaining transducers. When extensive signal averaging is performed, the data acquisition process can be quite time-consuming, especially for metallic components that require a low repetition rate to allow signals to die out. Such a long data acquisition time is particularly problematic if environmental and operational conditions are changing while data are being acquired. To reduce the total data acquisition time, proposed here is a methodology whereby multiple transmitters are simultaneously triggered, and each transmitter is driven with a unique excitation. The simultaneously transmitted waves are captured by one or more receivers, and their responses are processed by dispersion-compensated filtering to extract the response from each individual transmitter. The excitation sequences are constructed by concatenating a series of chirps whose start and stop frequencies are randomly selected from a specified range. The process is optimized using a Monte-Carlo approach to select sequences with impulse-like autocorrelations and relatively flat cross-correlations. The efficacy of the proposed methodology is evaluated by several metrics and is experimentally demonstrated with sparse array imaging of simulated damage.

Quantitative sparse array vascular elastography: the impact of tissue attenuation and modulus contrast on performance.

Quantitative sparse array vascular elastography visualizes the shear modulus distribution within vascular tissues, information that clinicans could use to reduce the number of strokes each year. However, the low transmit power sparse array (SA) imaging could hamper the clinical usefulness of the resulting elastograms. In this study, we evaluated the performance of modulus elastograms recovered from simulated and physical vessel phantoms with varying attenuation coefficients (0.6, 1.5, and [Formula: see text]) and modulus contrasts ([Formula: see text], [Formula: see text], and [Formula: see text]) using SA imaging relative to those obtained with conventional linear array (CLA) and plane-wave (PW) imaging techniques. Plaques were visible in all modulus elastograms, but those produced using SA and PW contained less artifacts. The modulus contrast-to-noise ratio decreased rapidly with increasing modulus contrast and attenuation coefficient, but more quickly when SA imaging was performed than for CLA or PW. The errors incurred varied from 10.9% to 24% (CLA), 1.8% to 12% (SA), and [Formula: see text] (PW). Modulus elastograms produced with SA and PW imagings were not significantly different ([Formula: see text]). Despite the low transmit power, SA imaging can produce useful modulus elastograms in superficial organs, such as the carotid artery.

Hybrid SIMO and MIMO sparse array radar

This paper clarifies what we benefit from single-input–multiple-output (SIMO) or multiple-input–multiple-output (MIMO) radar. We have developed an X-band sparse array imaging radar system capable of operating at both SIMO and MIMO modes. The hybrid radar modes are realized without any modification in hardware, but simply by switching the scheme of waveform generation and post-processing. A comparison has been made between the SIMO mode adopting a chirp pulse waveform and the MIMO mode based on the code-division multiple access method using the Gold-coded pulse waveform. Mutually complementary properties between the SIMO and MIMO modes in terms of the cost of computation, the ease of array calibration, and the detectability of targets are clarified through simulations and an experiment.

Sparse array imaging for microwave gauging by compressed sensing

The reliability of microwave level gauging can be improved by radar imaging techniques. An antenna array with a large aperture must be used, in order to achieve the desired resolution. At the same time, the number of array elements is limited to only a few, which leads to ambiguities due to spatial undersampling. The ambiguities can be resolved by application of compressed sensing (CS) techniques, as this paper will demonstrate. A model of this particular problem is developed, such that CS algorithms can be applied. Statistical analyses demonstrate the robustness of the method. Finally, measurements of a frequency modulated continuous wave (FMCW) system are presented, with an array size of down to 4 elements.

Noninvasive vascular elastography using plane-wave and sparse-array imaging

Stroke may occur when an atherosclerotic plaque ruptures in the carotid artery. Noninvasive vascular elastography (NIVE) visualizes the strain distribution within the carotid artery, which is related to its mechanical properties that govern plaque rupture. Strain elastograms obtained from the transverse plane of the carotid artery are difficult to interpret, because strain is estimated in Cartesian coordinates. Sparsearray (SA) elastography overcomes this problem by transforming shear and normal strain to polar coordinates. However, the SA's transmit power may be too weak to produce useful elastograms in the clinical setting. Consequently, we are exploring other imaging methods to solve this potential problem. This study evaluated the quality of elastograms produced with SA imaging, plane-wave (PW) imaging, and compounded-plane-wave (CPW) imaging. We performed studies on simulated and physical vessel phantoms, and the carotid artery of a healthy volunteer. All echo imaging was performed with a linear transducer array that contained 128 elements, operating at 5 MHz. In SA imaging, 7 elements were fired during transmission, but all 128 elements were active during reception. In PW imaging, all 128 elements were active during both transmission and reception. We created CPW images by steering the acoustic beam within the range of -15° to 15° in increments of 5°. SA radial and circumferential strain elastograms were comparable to those produced using PW and CPW imaging. Additionally, side-lobe levels incurred during SA imaging were 20 dB lower than those produced during PW imaging, and 10 dB lower than those computed using CPW imaging. Overall, SA imaging performs well in vivo; therefore, we plan to improve the technique and perform preclinical studies.

FMCW sparse array imaging and restoration for microwave gauging

Abstract. The application of imaging radar to microwave level gauging represents a prospect of increasing the reliability of target detection. The aperture size of the used sensor determines the underlying azimuthal resolution. In consequence, when FMCW-based multistatic radar (FMCW: frequency modulated continuous wave) is used, the number of antennas dictates this essential property of an imaging system. The application of a sparse array leads to an improvement of the azimuthal resolution by keeping the number of array elements constant with the cost of increased side lobe level. Therefore, ambiguities occur within the imaging process. This problem can be modelled by a point spread function (PSF) which is common in image processing. Hence, an inverse system to the imaging system is needed to restore unique information of existing targets within the observed radar scenario. In general, the process of imaging is of ill-conditioned nature and therefore appropriate algorithms have to be applied. The present paper first develops the degradation model, namely PSF, of an imaging system based on a uniform linear array in time domain. As a result, range and azimuth dimensions are interdependent and the process of imaging has to be reformulated in one dimension. Matrix-based approaches can be adopted in this way. The second part applies two computational methods to the given inverse problem, namely quadratic and non-quadratic regularization. Notably, the second one exhibits an ability to suppress ambiguities. This can be demonstrated with the results of both, simulations and measurements, and enables sparse array imaging to localize point targets more unambiguously.

A differential equations approach to l1-minimization with applications to array imaging

We present an ordinary differential equation approach to the analysis of algorithms for constructing l1 minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The connection to the discrete algorithms is provided by the Crandall–Liggett theory of monotone nonlinear semigroups. We illustrate the effectiveness of the discrete optimization algorithm in some sparse array imaging problems.

Development of Lamb Waves-Based SHM Systems

Guided waves (GW) based methods are a promising tool for structural health monitoring (SHM) of plate-like metallic and composite structures in which high safety standards are required. In this paper we present research with the aim to design and manufacture a prototype of Lamb waves (LW) SHM system. Two approaches can be applied for SHM of plate-like structures. One of them can be based on a sparse array and damage imaging involving incoherent summation of signals envelope. The second approach involves phased arrays with transducers spaced at a distance lower than half wavelength of the excited Lamb-mode. The influence of an arrays parameters on beamforming of Lamb waves is discussed in the case of linear array. It appears that an unequivocal localization of damage on a plate requires a 2D arrays topology; therefore a star-shaped active array was designed and manufactured for the developed SHM system. Two signal processing approaches were applied for that array, the standard one, based on the delay and sum (DAS) synthetic aperture focusing scheme, and the second one, using a self-focusing technique to obtain the separate images for each scatterer existing in the plate.

Shear lag solution for tuning ultrasonic piezoelectric wafer active sensors with applications to Lamb wave array imaging

An analytical investigation of the interaction between piezoelectric wafer active sensor (PWAS), guided Lamb waves, and host structure is presented in this paper, supported with application examples. The analytical investigation assumes a PWAS transducer bonded to the upper surface of an isotropic flat plate. Shear lag transfer of tractions and strains is assumed, and an analytical solution using the space-wise Fourier transform is reviewed, closed-form solutions are presented for the case of both ideal bonding (i.e., load transfer mechanism localized at the PWAS boundary) and not ideal bonding (i.e., load transfer mechanism localized close the PWAS boundary). The analytical solutions are used to derive Lamb wave mode tuning curves which indicate that frequencies exist at which the A0 mode or the S0 mode can be either suppressed or enhanced. The paper further shows that the capability to excite only one desired Lamb wave mode is critical for practical structural health monitoring applications such as PWAS phased array technique (e.g., the embedded ultrasonics structural radar, EUSR) and the sparse array imaging. Extensive experimental tests that verify the tuning mechanism and prediction curves are reported. Examples of correctly tuned EUSR images vs. detuned cases illustrate the paramount importance of Lamb wave mode tuning for the success of PWAS based damage detection.