An experimental study of compressed-sensing (CS) reconstruction of wideband near-field synthetic aperture radar (SAR) measurements for nondestructive evaluation found that reconstruction quality of the nonlinear conjugate-gradient CS algorithm (CG-CS) is highly sensitive to the hand-picked wavelet sparse-representation matrix, with acceptable images down to 15% spatial sampling (and detection down to 5%–15%) only when the basis is well matched to the scene. The study left open how to select or learn this representation automatically so that performance generalizes across scene types, materials, and frequencies, what the operational lower sampling limits and robustness bounds are, and how to replace random undersampling with optimized or adaptive sampling. Later work has narrowed pieces of this problem (sampling-operator design at 6.25% sampling, one-bit sparse imaging, task-driven sensing, deep-image-prior reconstruction in simulation) and a 2026 review still names real-time sparse-sampling near-field SAR with cross-scenario robustness as an open challenge; no published procedure closes the central basis-generalization question on measured data, so the problem remains open.

Background

Synthetic aperture radar (SAR) reconstructs a scene's reflectivity from phase-coherent, frequency-swept microwave measurements gathered while an antenna moves relative to the specimen; in near-field SAR for nondestructive evaluation (NDE, inspection of materials and structures without damaging them), the antenna scans a small aperture close to the specimen under test (SUT), and wideband (frequency-swept) signals give high range and cross-range resolution of internal structure. High spatial resolution normally requires sampling the measurement aperture at or above the Nyquist density, which forces long raster scans or large antenna arrays. Simple remedies — zero-filling (ZF, interpolating missing spatial samples with zeros) and the nonuniform fast Fourier transform (NUFFT, an FFT generalized to irregular sample locations) — alias and artifact when sampling is substantially reduced. Compressed sensing (CS) instead reconstructs the image from far fewer spatial samples by solving an underdetermined linear inverse problem under a sparsity constraint in some transform domain: if the image g\mathbf{g} is sparse (or compressible) in the range of a sparse-representation matrix Ψ\boldsymbol{\Psi} (typically a wavelet basis), greedy pursuits such as orthogonal matching pursuit (OMP, which iteratively selects the strongest sparse components) or optimization methods such as the nonlinear conjugate-gradient algorithm with a sparsity prior (CG-CS) can recover it from randomly undersampled measurements. Reconstruction quality is scored by structural similarity (SSIM, an image-similarity index) and peak signal-to-noise ratio (PSNR) against the fully sampled reconstruction. Yang, Zheng, Ghasr, and Donnell (IEEE Trans. Instrum. Meas. 2017) reported the experimental comparison of ZF, NUFFT, OMP-CS, and CG-CS on measured wideband near-field SAR data of rock-tray specimens (including a foil-wrapped rock) at 10%–60% random spatial undersampling, plus an enhanced Otsu-thresholding detector (Otsu's method picks a global grayscale threshold by maximizing between-class variance) for locating the conducting target; those detection experiments were simplified, reconstructing from only the first half of the frequency slides and substituting the identity sparse matrix for a wavelet basis. Their findings: CS methods give acceptable images at about 30% sampling where ZF/NUFFT need about 50%; with a well-chosen wavelet basis, CG-CS remains usable down to about 15% and strong scatterers are detectable at 5%–15%; OMP-CS does relatively better on dense scenes and CG-CS on sparse ones. Crucially, CG-CS performance varied widely across the seven tested wavelet families (Battle, Beylkin, Daubechies, Coiflet, Haar, Vaidyanathan, Symmlet), and the basis was chosen by trial for each scene. This basis sensitivity is the crux: CS guarantees and practical performance hinge on the sparsity of the true scene in the chosen Ψ\boldsymbol{\Psi}, yet natural NDE scenes (varied materials, shapes, and scattering contrasts) have no known universally good wavelet basis, and evaluating multiple bases per scene is itself computationally costly. The same study identified the companion gaps that motivate the problem here: the lowest sampling rate at which reconstruction and detection remain reliable (below the tested 5%–15% detection range) was uncharacterized, robustness across a broader variety of SUT materials and contrasts was untested, and the undersampling was purely random rather than designed — no adaptive or optimized measurement-selection strategy was coupled to the CS reconstruction. Related open threads appear across microwave imaging: dictionary learning (data-driven sparse representations learned from measurements rather than fixed bases) has been applied to far-field inverse SAR, and physics-constrained deep image priors (untrained neural networks whose parameters are optimized per scene to enforce measurement consistency) have been proposed for sparse near-field millimeter-wave SAR in simulation, but neither establishes an automatic representation-selection procedure validated on measured wideband near-field SAR data across scenes and frequencies.

Problem Statement

For CS-based wideband near-field SAR imaging and detection of the kind demonstrated by Yang et al. (2017), establish a principled, automatic procedure for selecting or learning the sparse-representation matrix Ψ\boldsymbol{\Psi} (or an equivalent sparsity prior) used in regularized reconstruction such as CG-CS, so that reconstruction and detection quality is preserved without per-scene manual basis tuning and generalizes across scene types, specimen materials and scattering contrasts, and operating frequencies — together with characterizing, on measured data, the operational lower limit of reliable reconstruction and detection as sampling rate decreases (including failure modes below the 5%–15% detection regime tested in the source) and replacing purely random spatial undersampling with an optimized or adaptive sampling design that is coupled to the CS reconstruction and detection objective. Computational tractability for practical (real-time or large-aperture) deployment and evaluation of the detection pipeline without the source study's simplifications are part of the same deployment objective: the common objective is dependable CS near-field SAR inspection at minimal measurement cost, with no component requiring hand-tuned, scene-specific sparse-basis choices.

This objective has three jointly required components: (i) the automatic procedure for selecting or learning Ψ\boldsymbol{\Psi} (or an equivalent sparsity prior) that generalizes across scene types, specimen materials and scattering contrasts, and operating frequencies without per-scene tuning; (ii) a measured-data characterization of the operational lower sampling limit — where "reliable" reconstruction and detection means quality measured against the fully sampled reconstruction by SSIM/PSNR, together with detection of the conducting target, as described above — including failure modes below the tested 5%–15% detection regime, with the measured data being of the kind demonstrated by the source and newly collected rather than the source's own specimens; and (iii) the sampling design that replaces purely random undersampling and is coupled to the CS reconstruction and detection objective.

References

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