An augmented Lagrangian trust region method for inclusion boundary reconstruction using ultrasound/electrical dual-modality tomography

Abstract

The ultrasound/electrical dual-modality tomography utilizes the complementarity of ultrasound reflection tomography (URT) and electrical impedance tomography (EIT) to improve the speed and accuracy of image reconstruction. Due to its advantages of no-invasive, no-radiation and low-cost, ultrasound/electrical dual-modality tomography has attracted much attention in the field of dual-modality imaging and has many potential applications in industrial and biomedical imaging. However, the data fusion of URT and EIT is difficult due to their different theoretical foundations and measurement principles. The most commonly used data fusion strategy in ultrasound/electrical dual-modality tomography is incorporating the structured information extracted from the URT into the EIT image reconstruction process through a pixel-based constraint. Due to the inherent non-linearity and ill-posedness of EIT, the reconstructed images from the strategy suffer from the low resolution, especially at the boundary of the observed inclusions. To improve this condition, an augmented Lagrangian trust region method is proposed to directly reconstruct the shapes of the inclusions from the ultrasound/electrical dual-modality measurements. In the proposed method, the shape of the target inclusion is parameterized by a radial shape model whose coefficients are used as the shape parameters. Then, the dual-modality shape inversion problem is formulated by an energy minimization problem in which the energy function derived from EIT is constrained by an ultrasound measurements model through an equality constraint equation. Finally, the optimal shape parameters associated with the optimal inclusion shape guesses are determined by minimizing the constrained cost function using the augmented Lagrangian trust region method. To evaluate the proposed method, numerical tests are carried out. Compared with single modality EIT, the proposed dual-modality inclusion boundary reconstruction method has a higher accuracy and is more robust to the measurement noise.