Single frequency inverse obstacle scattering: a sparsity constrained linear sampling method approach.

Area of Science:

• Electromagnetics and wave propagation
• Inverse problems and computational imaging
• Signal processing for remote sensing

Background:

• Linear sampling method (LSM) is an alternative to filtered backprojection (FBP) for obstacle imaging.
• Reconstructing obstacles from sparse far-field data at a single frequency is challenging.
• Tikhonov regularization in LSM yields poor obstacle boundary recovery with sparse data.

Purpose of the Study:

• To develop and evaluate a novel regularization strategy for LSM in obstacle imaging.
• To improve the accuracy of obstacle boundary reconstruction using sparse aperture data.
• To compare the performance of the new method against FBP and Tikhonov-regularized LSM.

Main Methods:

• Development of two regularization approaches based on constraining the sparsity of the solution's spatial gradient.
• Numerical comparison of the proposed method with FBP.
• Numerical comparison of the proposed method with Tikhonov-regularized LSM.

Main Results:

• The proposed spatial gradient regularization significantly improves obstacle recovery with sparse-aperture data.
• The new method demonstrates enhanced accuracy in reconstructing concave obstacles.
• The developed approach accounts for aspect-dependent scattering, leading to better image fidelity.

Conclusions:

• Spatial gradient sparsity regularization is a superior alternative to Tikhonov regularization for LSM in sparse data scenarios.
• The proposed method offers improved obstacle imaging capabilities, particularly for complex shapes.
• This work advances the field of inverse scattering problems and sparse data imaging.