Joint wavenumber- and spatial-domain sparse representation: A unified framework for guided wavefield reconstruction

This short communication proposes a joint wavenumber- and spatial-domain compressed sensing (JWSCS) framework for guided wavefield reconstruction. Existing sparse reconstruction methods typically operate in either the wavenumber domain or the spatial domain, each exploiting only one type of sparsity prior and exhibiting a lack of robustness against different damage scales. The proposed JWSCS framework simultaneously leverages wavenumber-domain modal sparsity and spatial-domain damage-induced sparsity. A joint sparse representation model is first established to integrate the spatial and wavenumber characteristics of the wavefield signals. A unified compressed sensing (CS) problem is then formulated, where a weighting coefficient is introduced to balance the sparsity constraints between the two domains. The non-convex problem is relaxed into a weighted ℓ₁-minimization problem and efficiently solved via convex optimization. Simulation and experimental results validate that the proposed JWSCS framework enables more accurate wavefield reconstruction with significantly fewer measurements than conventional single-domain CS methods. On real measured data at 70% sample compressive ratio, JWSCS achieves an average Pearson correlation coefficient of 0.88 ± 0.02, improving by approximately 7% and 17% compared with wavenumber-domain and spatial-domain CS, respectively.