On the usage of the Sparse Fourier Transform in ultrasound propagation simulation

Abstract

The Fourier transform is an algorithm for transforming the signal from the space/time domain into the frequency domain. This algorithm is essential for applications like image processing, communication, medicine, differential equations solvers, and many others. In some of these applications, most of the Fourier coefficients are small or equal to zero. This property of the signals is used by the Sparse Fourier transform which estimates significant coefficients of the signal with a lower time complexity than the Fourier transform. The goal of this paper is to evaluate available implementations of the Sparse Fourier transform on a set of benchmarks solving the ultrasound wave propagation in 1D, 2D, and 3D heterogeneous media. The results show that the fastest available implementation in 1D domains is MSFFT, however, it is not possible to use it in our implementation of the 2D Sparse Fourier transform. Thus the AAFFT 0.9 is selected for our implementation of the 2D Sparse Fourier transform as the most stable and acceptably fast implementation. The results on 3D simulation data show, that by using the SpFFT library it is possible to reduce the computation time of the Fourier transform in ultrasound wave propagation simulation.

The Fourier transform is an algorithm for transforming the signal from the space/time domain into the frequency domain. This algorithm is essential for applications like image processing, communication, medicine, differential equations solvers, and many others. In some of these applications, most of the Fourier coefficients are small or equal to zero. This property of the signals is used by the Sparse Fourier transform which estimates significant coefficients of the signal with a lower time complexity than the Fourier transform. The goal of this paper is to evaluate available implementations of the Sparse Fourier transform on a set of benchmarks solving the ultrasound wave propagation in 1D, 2D, and 3D heterogeneous media. The results show that the fastest available implementation in 1D domains is MSFFT, however, it is not possible to use it in our implementation of the 2D Sparse Fourier transform. Thus the AAFFT 0.9 is selected for our implementation of the 2D Sparse Fourier transform as the most stable and acceptably fast implementation. The results on 3D simulation data show, that by using the SpFFT library it is possible to reduce the computation time of the Fourier transform in ultrasound wave propagation simulation.