TY - JOUR

T1 - Density imaging using a multiple-frequency DBIM approach

AU - Lavarello, Roberto

AU - Oelze, Michael

PY - 2010/11

Y1 - 2010/11

N2 - Current inverse scattering methods for quantitative density imaging have limitations that keep them from practical experimental implementations. In this work, an improved approach, termed the multiple-frequency distorted Born iterative method (MF-DBIM) algorithm, was developed for imaging density variations. The MF-DBIM approach consists of inverting the wave equation by solving for a single function that depends on both sound speed and density variations at multiple frequencies. Density information was isolated by using a linear combination of the reconstructed single-frequency profiles. Reconstructions of targets using MF-DBIM from simulated data were compared with reconstructions using methods currently available in the literature, i.e., the dual-frequency DBIM (DF-DBIM) and T-matrix approaches. Useful density reconstructions, i.e., root mean square errors (RMSEs) less than 30%, were obtained with MF-DBIM even with 2% Gaussian noise in the simulated data and using frequency ranges spanning less than an order of magnitude. Therefore, the MFDBIM approach outperformed both the DF-DBIM method (which has problems converging with noise even an order of magnitude smaller) and the T-matrix method (which requires a ka factor close to unity to achieve convergence). However, the convergence of all the density imaging algorithms was compromised when imaging targets with object functions exhibiting high spatial frequency content.

AB - Current inverse scattering methods for quantitative density imaging have limitations that keep them from practical experimental implementations. In this work, an improved approach, termed the multiple-frequency distorted Born iterative method (MF-DBIM) algorithm, was developed for imaging density variations. The MF-DBIM approach consists of inverting the wave equation by solving for a single function that depends on both sound speed and density variations at multiple frequencies. Density information was isolated by using a linear combination of the reconstructed single-frequency profiles. Reconstructions of targets using MF-DBIM from simulated data were compared with reconstructions using methods currently available in the literature, i.e., the dual-frequency DBIM (DF-DBIM) and T-matrix approaches. Useful density reconstructions, i.e., root mean square errors (RMSEs) less than 30%, were obtained with MF-DBIM even with 2% Gaussian noise in the simulated data and using frequency ranges spanning less than an order of magnitude. Therefore, the MFDBIM approach outperformed both the DF-DBIM method (which has problems converging with noise even an order of magnitude smaller) and the T-matrix method (which requires a ka factor close to unity to achieve convergence). However, the convergence of all the density imaging algorithms was compromised when imaging targets with object functions exhibiting high spatial frequency content.

UR - http://www.scopus.com/inward/record.url?scp=78149242133&partnerID=8YFLogxK

U2 - 10.1109/TUFFC.2010.1713

DO - 10.1109/TUFFC.2010.1713

M3 - Article

C2 - 21041134

AN - SCOPUS:78149242133

SN - 0885-3010

VL - 57

SP - 2471

EP - 2479

JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

IS - 11

M1 - 5611694

ER -