Sparse virtual wave thermography for nondestructive evaluation using orthogonal matching pursuit

Active thermography suffers from depth-dependent blurring because heat transport is diffusive. The virtual wave concept (VWC) mitigates this limitation by transforming measured thermal transients into propagative, wave-like signals, enabling the use of established ultrasonic and radar imaging tools (e.g. synthetic-aperture focusing and time reversal). The VWC transformation, however, requires solving an ill-posed inverse problem and therefore relies on regularized inversion; ℓ 2 − and ℓ 1 -regularized solutions have been reported, with ℓ 1 typically providing sharper reconstructions at the expense of iterative optimization and parameter tuning. Here we introduce an ℓ 0 -regularized VWC inversion based on orthogonal matching pursuit (OMP). The proposed approach yields sparser, higher-contrast, and better-localized virtual-wave reconstructions than ℓ 1 regularization while maintaining a computational cost comparable to ℓ 2 regularization. We validated the method on COMSOL simulations and LED long-pulse experiments on a PMMA specimen with flat-bottom holes at multiple depths, demonstrating improved defect contrast and depth estimation suitable for real-time thermographic nondestructive evaluation.