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Three-dimensional (3-D) imaging sonar systems require large planar arrays, which incur hardware costs. In contrast, a cross array consisting of two perpendicular linear arrays can also support 3-D imaging while dramatically reducing the number of sensors. Moreover, the use of an aperiodic sparse array can further reduce the number of sensors efficiently. In this paper, an optimized method for sparse cross array synthesis is proposed. First, the beamforming of a cross array based on a multi-frequency algorithm is simplified for both near-field and far-field. Next, a perturbed convex optimization algorithm is proposed for sparse cross array synthesis. The method based on convex optimization utilizes a first-order Taylor expansion to create position perturbations that can optimize the beam pattern and minimize the number of active sensors. Finally, a cross array with 100 + 100 sensors is employed from which a sparse cross array with 45 + 45 sensors is obtained via the proposed method. The experimental results show that the proposed method is more effective than existing methods for obtaining optimum results for sparse cross array synthesis in both the near-field and far-field.

Three-dimensional (3-D) localization information, including elevation angle, azimuth angle, and range, is important for locating a single source with spherical wave-fronts. Aiming to reduce the high computational complexity of the classical 3-D multiple signal classification (3D-MUSIC) localization method, a novel low-complexity reduced-dimension MUSIC (RD-MUSIC) algorithm based on the sparse symmetric cross array (SSCA) is proposed in this article. The RD-MUSIC converts the 3-D exhaustive search into three one-dimensional (1-D) searches, where two of them are obtained by a two-stage reduced-dimension method to find the angles, and the remaining one is utilized to obtain the range. In addition, a detailed complexity analysis is provided. Simulation results demonstrate that the performance of the proposed algorithm is extremely close to that of the existing rank-reduced MUSIC (RARE-MUSIC) and 3D-MUSIC algorithms, whereas the complexity of the proposed method is significantly lower than that of the others, which is a big advantage in practice.

Nowadays, sparse arrays have been a hotspot for research in the direction of arrival (DOA). In order to achieve a big value for degrees of freedom (DOFs) using spatial smoothing methods, researchers try to use multiple uniform linear arrays (ULAs) to construct sparse arrays. But, with the number of subarrays increasing, the complexity also increases. Hence, in this paper, a design method, named as the cross-coarray consecutive-connected (4C) criterion, and the sparse array using Q ULAs (SA-UQ) are proposed. We first analyze the virtual sensor distribution of SA-U2 and extend the conclusions to SA-UQ, which is the 4C criterion. Then, we give an algorithm to solve the displacement between subarrays under the given Q ULAs. At last, we consider a special case, SA-U3. Through the analysis of DOFs, SA-UQ can find underdetermined signals. Moreover, SA-U3 can obtain DOFs close to other sparse arrays using three ULAs. The simulation experiments prove the performance of SA-UQ.

H-scan ultrasound (US) is a high-resolution imaging technique for soft tissue characterization. By acquiring data in volume space, H-scan US can provide insight into subtle tissue changes or heterogenous patterns that might be missed using traditional cross-sectional US imaging approaches. In this study, we introduce a 3-dimensional (3-D) H-scan US imaging technology for voxel-level tissue characterization in simulation and experimentation. Using a matrix array transducer, H-scan US imaging was developed to evaluate the relative size of US scattering aggregates in volume space. Experimental data was acquired using a programmable US system (Vantage 256, Verasonics Inc, Kirkland, WA) equipped with a 1024-element (32 × 32) matrix array transducer (Vermon Inc, Tours, France). Imaging was performed using the full array in transmission. Radiofrequency (RF) data sequences were collected using a sparse random aperture compounding technique with 6 different data compounding approaches. Plane wave imaging at five angles was performed at a center frequency of 8 MHz. Scan conversion and attenuation correction were applied. To generate the 3-D H-scan US images, a convolution filter bank (N = 256) was then used to process the RF data sequences and measure the spectral content of the backscattered US signals before volume reconstruction. Preliminary experimental studies were conducted using homogeneous phantom materials embedded with spherical US scatterers of varying diameter, i.e., 27 to 45, 63 to 75, or 106–126 μm. Both simulated and experimental results revealed that 3-D H-scan US images have a low spatial variance when tested with homogeneous phantom materials. Furthermore, H-scan US is considerably more sensitive than traditional B-mode US imaging for differentiating US scatterers of varying size (p = 0.001 and p = 0.93, respectively). Overall, this study demonstrates the feasibility of 3-D H-scan US imaging using a matrix array transducer for tissue characterization in volume space. •Simulations demonstrated feasibility of volumetric H-scan ultrasound (US) imaging using a matrix array transducer.•Different apodization methods were implemented and evaluated for maximal H-scan US image quality.•Sparse volumetric H-scan US imaging technique was shown to differentiate acoustic scatterers of varying size.

This paper focuses on the problem of the DOA estimation of coherent signals for the acoustic vector-sensor arrays (AVSAs) in the presence of the isotropic ambient noise. We propose a high-resolution DOA estimation method based on the acoustic intensity principle and the sparse representation technique. First, two cross-covariance matrices are constructed by employing the acoustic pressure and particle velocity components of the AVSA, which eliminates the isotropic noise. Then, in order to fully explore the DOA information of the particle velocity components, an augmented matrix is formed based on the two cross-covariance matrices. We observe an interesting fact that the left singular vector corresponding to the maximum singular value of the augmented cross-covariance matrix is the linear combination of all the signal steering vectors. Based on this fact, a high-resolution DOA estimation algorithm is developed via sparsely representing the left singular vector. This method does not require the prior knowledge of the noise variance or the number of signals to construct the sparse representation model. Simulation and experimental results demonstrate the proposed method outperforms the MUSIC method based on the forward/backward spatial smoothing and some existing sparse representation methods in estimation accuracy and angular resolution, especially in the cases of a low signal-to-noise ratio and/or coherent signals with small angular separations.

Underwater acoustic imaging employs a special form of array which includes numerous transducer elements to achieve beamforming. Although a large-scale array can bring high imaging resolution, it will also cause difficulties in hardware complexity and real-time application. In this paper, in order to reduce the number of array elements, a sparse optimization for Mills cross is proposed, considering the elements’ distributions and weights design. The improved genetic algorithm is adopted to generate evolutions for sparse solution. In order to ensure effective convergence and successful evolution, relevant genetic operators are proposed, including appropriate population coding, correct fitness function, reasonable selection strategy and efficient two-point orthogonal crossover, among others. Essentially, a satisfied sparse solution is a result of mutual restraint between array elements’ survivals and their weights. The simulations reveal that our sparse cross array decreases the number of elements by 8.25% compared to the conventional Mills cross multiplicative array, while keeping the advantages of narrow main lobe width and low sidelobe level. Improved genetic algorithm is an effective method for the underwater acoustic imaging array to implement the sparse optimization.

The ultrasonic phased array total focusing method (TFM) has the advantages of high imaging resolution and high sensitivity to small defects. However, it has a long imaging time and cannot realize near-distance defect imaging, which limits its application for industrial detection. A sparse-TFM algorithm is adopted in this work to solve the problem regarding rapid imaging of near- distance defects in thin plates. Green’s function is reconstructed through the cross-correlation of the diffuse full matrix captured by the ultrasonic phased array. The reconstructed full matrix recovers near-distance scattering information submerged by noise. A sparse array is applied to TFM for rapid imaging. In order to improve the imaging resolution, the location of active array elements in the sparse array can be optimized using the genetic algorithm (GA). Experiments are conducted on three aluminium plates with near-distance defects. The experimental results confirm that the sparse-TFM algorithm of Lamb waves can be used for near-distance defects imaging, which increases the computational efficiency by keeping the imaging accuracy. This paper provides a theoretical guidance for Lamb wave non-destructive testing of the near-distance defects in plate-like structures.

The automatic identification of underwater noncooperative targets without label records remains an arduous task considering the marine noise interference and the shortage of labeled samples. In particular, the data-driven mechanism of deep learning cannot identify false samples, aggravating the difficulty in noncooperative underwater target recognition. A semi-supervised ensemble framework based on vertical line array fusion and the sparse adversarial co-training algorithm is proposed to identify noncooperative targets effectively. The sound field cross-correlation compression (SCC) feature is developed to reduce noise and computational redundancy. Starting from an incomplete dataset, a joint adversarial autoencoder is constructed to extract the sparse features with source depth sensitivity, aiming to discover the unknown underwater targets. The adversarial prediction label is converted to initialize the joint co-forest, whose evaluation function is optimized by introducing adaptive confidence. The experiments prove the strong denoising performance, low mean square error, and high separability of SCC features. Compared with several state-of-the-art approaches, the numerical results illustrate the superiorities of the proposed method due to feature compression, secondary recognition, and decision fusion.

ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matrices and arrays that share various index sets defined by the factor levels. For many types of categorical factors, it is plausible that an ANOVA decomposition exhibits some consistency across orders of effects, in that the levels of a factor that have similar main-effect coefficients may also have similar coefficients in higher-order interaction terms. In such a case, estimation of the higher-order interactions should be improved by borrowing information from the main effects and lower-order interactions. To take advantage of such patterns, this article introduces a class of hierarchical prior distributions for collections of interaction arrays that can adapt to the presence of such interactions. These prior distributions are based on a type of array-variate normal distribution, for which a covariance matrix for each factor is estimated. This prior is able to adapt to potential similarities among the levels of a factor, and incorporate any such information into the estimation of the effects in which the factor appears. In the presence of such similarities, this prior is able to borrow information from well-estimated main effects and lower-order interactions to assist in the estimation of higher-order terms for which data information is limited.