Performance of the Linear Model Scattering of 2D Full Object with Limited Data.

Area of Science:

• Electromagnetics and Applied Physics
• Computational Imaging and Inverse Problems

Background:

• Inverse scattering problems are central to imaging applications like radar and geophysics.
• Practical limitations often restrict data acquisition, necessitating analysis with incomplete datasets.
• Reconstruction quality from limited data remains a key challenge in many scientific and engineering fields.

Purpose of the Study:

• To mathematically analyze and estimate the achievable resolution for object reconstruction using limited far-field scattering data.
• To investigate the impact of multi-view excitations at a single frequency on reconstruction resolution.
• To evaluate the Number of Degrees of Freedom (NDF) and Point Spread Function (PSF) for 2D rectangular geometries.

Main Methods:

• Mathematical analysis of inverse scattering problems with limited data.
• Numerical simulations for resolution estimation.
• Analytical and approximated closed-form evaluation of the Point Spread Function (PSF).
• Examination of different sensing modes (receiving, transmission, angle) to assess their impact on NDF and resolution.

Main Results:

• Analytical estimation of the Number of Degrees of Freedom (NDF) for 2D rectangular geometry.
• Comparison of approximated and exact Point Spread Functions (PSF).
• Demonstration of how different sensing modes affect NDF and resolution performance.
• Numerical validation of the resolution analysis for localizing point-like scatterers.

Conclusions:

• The study provides a framework for understanding resolution limits in inverse scattering with limited data.
• The analysis highlights the trade-offs between data availability, sensing modes, and achievable reconstruction resolution.
• Findings are applicable to optimizing imaging strategies in practical scenarios like radar and GPR.