Efficient ultrasonic phased array focused wave imaging using retrospective encoding and p-th root wavenumber-domain...

Ultrasonic phased array imaging is widely used in industrial non-destructive testing (NDT) due to its advantages of a flexible transmit-receive strategy, high sensitivity and excellent visualization. However, conventional ultrasonic phased array focused wave imaging offers high spatial resolution only near the focal point. Although the retrospective encoding for conventional ultrasound sequences (REFoCUS) technique can reconstruct equivalent full matrix capture (FMC) datasets from focused transmissions, the resulting images still suffer from the high computational cost and limited noise suppression capability of the total focusing method (TFM). To overcome these limitations, this study proposes an efficient and high-quality imaging approach termed retrospective encoding and pth root wavenumber-domain reconstruction (REpRWD). The proposed framework first applies REFoCUS to recover a localized high-energy FMC dataset from focused wave transmissions. Subsequently, a nonlinear pth root wavenumber-domain (pRWD) algorithm is introduced for image reconstruction. This strategy preserves the signal-to-noise ratio (SNR) enhancement capability of nonlinear beamforming while maintaining the low computational complexity of wavenumber-domain imaging, providing an additional pathway for high-quality ultrafast phased array imaging. Simulation and experimental results demonstrate that REpRWD achieves substantially improved computational efficiency. This performance advantage widens as the reconstruction pixel count grows. The method also provides superior image quality and improved accuracy in defect localization and characterization. These findings highlight its potential as a practical and powerful imaging technique for ultrasonic phased array NDT applications.