Imaging through coda wave interferometryvia sparse reconstruction

Abstract

The coda wave interferometry is widely used in the fields of geophysics and material science. As an extension of coda wave interferometry, imaging through coda wave interferometry is a technique to obtain the spatial distribution of small velocity perturbations within a scattering medium by using time lapse and sensitivity kernels in the diffusion approximation. However, imaging through coda wave interferometry is essentially an undetermined problem without definite solution, resulting in some difficulties in accurately locating small velocity perturbations within a scattering medium. Meanwhile, compressed sensing has been used in many physical imaging systems in recent years. In this paper, we present an imaging method through coda wave interferometry to solve aforementioned problems by using sparse reconstruction algorithm which is involved in compressed sensing theory. The sparsity of velocity perturbation in its space distribution is taken into account in the proposed method. Firstly, the undetermined equation for inversion imaging is established based on the time-lapse data obtained by coda wave interferometry and the sensitivity kernel matrix in the diffusion approximation. Secondly, the inversion equation is reconstructed by using the sparse transformation within the framework of compressed sensing theory. Finally, the minimization of <i>l</i>₁ norm is solved by the compressed sensing reconstruction algorithm, and the imaginary part for the spatial distribution of velocity perturbations is subsequently obtained. This method can accurately capture the spatial locations and ranges of both single velocity perturbation and multiple velocity perturbations in scattering medium with high computational efficiency. The numerical simulations are compared with the results from the existing linear least squares method, demonstrating that the proposed method can avoid the complex parameter determination operation, thus greatly improving the accuracy of inversion images, and also significantly reducing the calculating time.