arXiv subjects

Yisu Yan

Publications and source records attributed to Yisu Yan.

4 recordsLinked to original sources

arXiv2026

Observation Modeling of Reference--Background Residuals in Single-Snapshot FDA-MIMO-GPR

Reference media are widely used in distorted-Born-approximation-based GPR imaging to represent partially known propagation effects. When the true host background differs from the chosen reference medium, the difference enters the observations and propagates into anomaly estimates. For single-snapshot FDA-MIMO-GPR, this paper establishes a reference-state observation model under the distorted Born approximation and defines that difference as the reference--background medium residual, namely, the effective residual between the reference medium and the physical background medium. Hereafter, this quantity is abbreviated as the reference--background residual. Its response is derived from the Cole--Cole dispersive mapping, the reference propagation kernels, and the FDA frequency--transmit organization. The paper then constructs its observation-domain covariance, analyzes the off-diagonal channel-block structure, and uses a standard Tikhonov estimator to show how the response transfers to reconstruction error and covariance over an anomaly candidate region. Numerical results show pronounced cross-frequency and cross-channel covariance under mismatched reference states. After Tikhonov reconstruction, these structures appear as low-dimensional, concentrated pseudo-anomaly errors. Right-hand-side coherence and inter-channel correlation arise mainly because multiple transmit--receive channels jointly observe the same residual field, while FDA space-frequency coding determines their organization in the observation and reconstruction domains. The reference--background residual should therefore be modeled explicitly in reference-state selection, background suppression, and channel-covariance analysis for single-snapshot FDA-MIMO-GPR.

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arXiv2026

Weak-Fluctuation-Induced Clutter Covariance and Subspace Structure in Single-Snapshot FDA-MIMO GPR

Weak constitutive fluctuations in dispersive subsurface media can induce distributed clutter that reshapes the observation structure of ground-penetrating radar (GPR). This paper analyzes this effect for single-snapshot frequency-diverse array multiple-input multiple-output GPR. Focusing on medium-induced clutter, rather than on general target--clutter joint modeling, it establishes a statistical propagation chain from Cole--Cole parameter perturbations to electromagnetic contrast, first-order Born channel snapshots, clutter covariance, and subspace descriptors. A medium-aware snapshot model and a covariance propagation framework are then derived to characterize how constitutive uncertainty alters observation-domain spectral structure under a local weak-fluctuation regime. Numerical experiments verify the consistency of the proposed propagation relation under the adopted first-order Born and constitutive-linearization approximations. Within the tested setting, medium-induced clutter reshapes the eigenspectrum and changes target--clutter overlap metrics. Spatial correlation length and background-scene variation act as consistently strong structural drivers, while the FDA frequency increment also produces measurable changes in the normalized covariance geometry.

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arXiv2026

Medium-Induced Cross-Frequency Clutter Structure in Single-Snapshot FDA-MIMO-GPR With a Weak-Dispersion Criterion

This paper investigates the cross-frequency structure of background clutter induced by random dispersive media in single-snapshot FDA-MIMO-GPR. Representative media are modeled by the Cole--Cole formulation to relate dispersive constitutive behavior to the reference propagation environment and observation-domain statistics. A normalized incremental contrast function is introduced under a reference-medium framework, and a single-snapshot background-response expression with first-order propagation-kernel feedback is derived. Based on this expression, a cross-frequency coupling strength of the leading-order background covariance is defined. Numerical results show that, in weakly dispersive scenes, the proposed analysis remains consistent across constitutive mapping, the zeroth-order propagation skeleton, first-order distorted-Born truncation, propagation-kernel feedback, and single-channel response closure. The proposed metric distinguishes uncoupled and explicitly coupled constructions, remains stable under pure energy scaling, responds clearly to correlation length and relaxation-location parameters, and corresponds directly to the error of the frequency block-diagonal approximation. Additional experiments show that the resulting cross-frequency structure affects whitening and principal-subspace extraction. In scenes with pronounced relaxation, abrupt breakdown under strong perturbations and high-error plateaus indicate that the present theory is mainly applicable within the validity range of first-order feedback.

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arXiv2026

Linking Dispersive-Medium Uncertainty to Clutter Analysis in Single-Snapshot FDA-MIMO-GPR

Single-snapshot FDA-MIMO-GPR requires clutter models that account for dispersive-medium uncertainty, yet the statistical link between complex-medium characterization and clutter covariance analysis has remained unclear. This paper develops a propagation-side statistical framework that maps random perturbations of the relaxation spectrum to complex permittivity, complex wavenumber, steering-vector perturbation, medium-induced clutter covariance, and total clutter covariance. Within this framework, the effects of medium uncertainty on effective rank, effective clutter-subspace dimension, and target--clutter separability are characterized through a KL-based modal decomposition and a subspace-projection analysis. Numerical validation uses five literature-informed dielectric families to define physically traceable prior scenarios, a controlled random-field model to exercise the main propagation chain, and gprMax-based full-wave FDTD snapshots for an independent solver-level consistency check. Monte Carlo closure shows stage-wise numerical consistency, identifies steering linearization as the dominant approximation-sensitive step, and supports a weak perturbation regime with a bounded extension into a moderate regime. In a representative whitening-and-detection benchmark, the structured covariance model raises AUC from 0.593 for a diagonal baseline to 0.753, while prior-mismatch experiments indicate gradual rather than abrupt degradation. These results provide an explicit and interpretable interface for embedding complex-medium uncertainty into FDA-MIMO-GPR clutter analysis within a first-order, propagation-dominated setting.

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