Inverse Patch Transfer Function Method based on Steepest Gradient Descent Algorithm for Sound Field Reconstruction

Abstract

In the iPTF method with Green’s function, the classical regularization method used to solve the inverse problem can’t provide satisfactory reconstruction results around some eigen frequencies of the cavity in the iPTF method with Green’s function. In this paper, the steepest gradient descent (SGD) algorithm is introduced to solve the inverse problem in the iPTF method. In addition, to make the iPTF method with Green’s function more efficient, Contour-integration is used to split the Fourier series of Green’s function into one single-sum and one double-sum Fourier series. By applying Contour-integration, the computational efficiency of the iPTF method with Green’s function has been improved. The iPTF method with efficient Green’s function is examined in both simulations and application experiments. Experimental validations in the application are carried out in the end. The present results in experiments are also acceptable for field reconstruction.