Image reconstruction using eigenfunctions of a scattering operator

Abstract

A multiple-frequency iterative inverse scattering method is reviewed. In the method, scattered acoustic fields are described using a scattering operator with eigenfunctions that correspond to far-field patterns of an effective source distribution. Incident-wave patterns determined using the eigenfunctions focus on the distribution. The focusing properties of the eigenfunctions are employed to reconstruct an object by using products of numerically calculated fields defined by weighted products of the eigenfunctions. The full range of frequencies present in an incident pulse waveform is employed. Iteration using a linearized version of the method and calculated scattering from an estimate of the object permits reconstruction of large-scale high-contrast objects. The method is illustrated using calculated and measured data. In the calculations, an exact solution for scattering from nonconcentric lossy cylinders with parallel axes was employed to obtain the scattered field. In the measurements, a novel ring-transducer system was used to obtain the incident and total fields. The results of simulations and experiments show that the method converges and is accurate for high-contrast large-scale tissue-mimicking objects. Reconstructions using measured scattering from random media have considerably less speckle than conventional b-scan images, implying that the inverse scattering method can clearly demonstrate small high-contrast inclusions.