Fast and High-Resolution Acoustic Beamforming: A Convolution Accelerated Deconvolution Implementation

Abstract

It is valuable to improve the resolution and speed of acoustic beamforming in real-time measurement, especially fault location, noise mapping, and so on. However, multiplication of the power transfer matrix takes much time in the iteration of the deconvolution algorithm. This article proposes a novel method based on the convolution approximation and GPU platform to obtain acoustic imaging with a high resolution quickly. First, the power propagation matrix is approximated by a symmetric Toeplitz block Toeplitz (STBT) matrix, which can transform the product of matrix and vector into the convolution of two smaller patterns. Three different convolution kernels are derived for the convolution operation, including 2-D variant convolution kernel, 2-D invariant convolution kernel, and 1-D separable invariant convolution kernel. Then, the regularization deconvolution algorithm with the convolution kernel is derived. Besides, the relation between approximation error, time cost, and setting parameters is discussed. The results show that the separable invariant convolution kernel can obtain the fastest imaging and relatively accurate localization, while the time consumption of the variant kernel is the highest. Simulations and experiments are operated on the CPU and GPU to make a comparison, which validates that our proposed deconvolution-GPU implementation can significantly improve the computation speed for the matrix on a large scale.