The ultrasonic phased array total focusing method (TFM) has the advantages of high imaging signal-to-noise ratio (SNR) and high defect resolution, but the problem of large amount data capturing and processing limits its practical industrial applications. To reduce the imaging calculation demand of the total focusing method, a half-matrix focusing method (HFM) is proposed based on the acoustic reciprocity. The method simplifies the calculation process of full-matrix data capturing (FMC) and total focus imaging. The experimental results show that the signal obtained by the linear array transceiver sensor is highly consistent, and the imaging resolution and signal-to-noise ratio of the half-matrix focusing method are slightly lower than those of full-matrix focusing method and higher than those of the B-scan imaging. However, compared with TFM, data acquisition and computational efficiency using the HFM have been improved significantly.

Shallow underground acoustic source localization is a component of near-field source localization, which is involved in numerous application fields. The positioning accuracy is mainly limited by the accuracy of time of arrival (TOA)/time difference of arrival (TDOA) extraction and velocity extraction from noisy data. The steered response power with phase transform (SRP-PHAT) is one of the most robustness and high-precision acoustic source localization approaches, which avoids extracting the TDOA in advance. But SRP-PHAT is constrained for only using under known velocity. Furthermore, it is barely possible for shallow underground sound source localization to easily obtain high-quality velocity models. This paper proposes an improved SRP-PHAT with unknown velocity (SRP-PHAT-UNVEL), which avoids extracting the TDOA and velocity in advance. SRP-PHAT-UNVEL matches the calculated time delay curve with the actual time delay curve by scanning of the candidate spatial position and the candidate velocity simultaneously, so as to maximize the output energy to fulfill the positioning. However, SRP-PHAT-UNVEL has larger computational complexity as it proceeds with the optimization of space and velocity. Since the spatial position and velocity affect the shape and the curvature of the calculated delay curve respectively, these are two relatively independent processes. Therefore, the simultaneous optimization of space and velocity can be replaced by a two-stage optimization to improve the efficiency and accuracy of SRP-PHAT-UNVEL. Spatial optimization is equivalent to the optimization of SRP-PHAT, and the spatial optimization of the bat algorithm has faster convergence rate and higher location precision than traditional methods. Velocity optimization can be achieved by the common linear search technique since the function of velocity and energy is an ideal convex function. Simulation experiment results show that the proposed method is insensitive to noise, which can achieve high accuracy of the acoustic source position and velocity simultaneously. With grouping the measured data, the proposed method can further improve the robustness and accuracy by fusing the grouping location results with principal component analysis.

High-precision source localization depends on many factors, including a suitable location method. Beamforming-based methods, such as the steered response power (SRP), are a common type of acoustic localization methods. However, these methods have low spatial resolution. The SRP method with phase transform (SRP-PHAT) improves the spatial resolution of SRP and is one of the most effective and robust methods for source localization. However, the introduction of a phase transform to SRP might amplify the power of the noise and result in many local extrema in the SRP space, which has a negative impact on source localization. In this paper, a steered sample algorithm (SSA) based on the reciprocity of wave propagation for acoustic source localization is proposed. The SSA localization process is similar to the hyperbolic Radon transform, which is theoretically analyzed and is the most essential difference form the SRP/SRP-PHAT. Compared with the SRP-PHAT, the experimental results demonstrate that the SSA perform better when it comes to array signal positioning with limited array elements and narrow azimuth signal, where SSA can achieve high precision positioning with lower SNR.

Tomography has been widely used in many fields. The theoretical basis of tomography is the Radon transform, which is the line integral along a radial line oriented at a specific angle. In practice, the detector that collects the projection has a certain width, which does not coincide with the line integral. Therefore, the resolution of the reconstructed image will be reduced. In order to overcome the effect of the detector width on the reconstruction quality, some reconstruction methods have taken the influence of the detector width into account and have achieved high reconstruction quality, such as the distance-driven model (DDM) and the area integral model (AIM). They have no exact analytic inversion formula, just numerical processing means to improve the reconstruction quality. According to the characteristics of DDM and AIM projection functions, a new integral transform is established, which is called Gaussian weighted Radon transform (GWRT). The width of integral line can be controlled by parameter in GWRT. GWRT is the generalized Radon transform in theory. We derive the analytical inversion formula of GWRT and establish a new numerical inversion algorithm based on it, i.e. optimized FBP. GWRT has a perfect theoretical framework, which can realize the accurate inversion of integral transform with integral line of a certain width. The experimental results show that the GWRT is feasible, and the image reconstruction quality is higher when the detector has a certain width than that of Radon transform implemented by FBP. And GWRT has better anti-noise ability than Radon transform.