Computational efficiency of ultrasonic guided wave imaging algorithms

Guided wave imaging techniques employed for structural health monitoring (SHM) can be computationally demanding, especially for adaptive techniques such as minimum variance distortionless response (MVDR) imaging, which requires a matrix inversion for each pixel calculation. Instantaneous windowing has been shown in previous work to improve guided wave imaging performance. The use of instantaneous windowing has the additional benefit of significantly reducing the computational requirements of image generation. This paper derives a formulation for MVDR imaging using instantaneous windowing and shows that the matrix inversion associated with MVDR imaging can be optimized, reducing the computational complexity to that of conventional delay-and-sum imaging algorithms. Additionally, a vectorized approach is presented for implementing guided wave imaging algorithms, including delay-and-sum imaging, in matrix-based software packages. The improvements in computational efficiency are quantified by measuring computation time for different array sizes, windowing assumptions, and imaging methods.