Stratigraphic reconstruction from terahertz and ultrasonic signals by deconvolution: A review

Nondestructive evaluation techniques, such as terahertz and ultrasonic testing, use short pulses to probe layered materials and reconstruct their stratigraphy by analyzing time delays between echoes at internal interfaces. However, when layers are sufficiently thin, successive echoes temporally overlap, making direct identification of their number and timing challenging. In such cases, deconvolution techniques are employed to extract the impulse response or key features such as echo locations and amplitudes, improving resolution of the local stratigraphy. This review examines four widely used deconvolution algorithms for stratigraphic reconstruction under the assumption of a sparse impulse response, where layer boundaries are modeled as discrete, sharp echoes. Two time-domain methods—orthogonal matching pursuit and ${\ell }_1$-norm-based sparse deconvolution—and two frequency-domain approaches—multiple signal classification and autoregressive spectral extrapolation—are discussed. Their theoretical foundations, practical implementation, and comparative performance are evaluated using synthetic signals and experimental echograms from terahertz pulsed imaging and ultrasound sonography. These techniques enhance the ability to distinguish closely spaced interfaces and are applicable to defect detection in materials, tissue-layer analysis in medical diagnostics, and preprocessing for 3D imaging.