A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
IEEE Transactions on Image Processing
A study of numerical methods for the level set approach
Applied Numerical Mathematics
Subspace-based localization and inverse scattering of multiply scattering point targets
EURASIP Journal on Applied Signal Processing
Asymptotic Imaging of Perfectly Conducting Cracks
SIAM Journal on Scientific Computing
Reinterpretation and Enhancement of Signal-Subspace-Based Imaging Methods for Extended Scatterers
SIAM Journal on Imaging Sciences
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In this paper, we study how to image both the location and the shape of extended targets using the response matrix obtained from inter-element response of an active array of transducers. In particular, the time reversal technique is used for efficient initial localization of the target and the level set method is used for shape reconstruction. We then show how to couple the location estimation and shape reconstruction in a complementary way to improve accuracy for range estimation. Resolution analysis for active arrays in remote sensing regime is also presented. We illustrate with numerical experiments which show that the method is capable of imaging objects with complicated shapes and that the method is robust with respect to noisy data.