Super-resolution algorithms for ultrasonic nondestructive evaluation imagery

The spatio‐temporal range resolution of ultrasonic measurements is often severely limited by the inherent band‐limited spectral transfer function of ultrasonic transducers. This is manifested as ringing in the time domain. Super‐resolution algorithms and a new MATLAB‐based software system are presented for improving spatial resolution in one‐dimensional (1‐D) pulse‐echo signals (A‐scans). Two‐dimensional (2‐D) images (B‐scans) and 3‐D volumes are formed from suites of processed 1‐D signals. The algorithms solve two inverse problems that are ill‐posed and ill‐conditioned. Regularization techniques and prior constraints are used to ensure useful results in practice. Given a noisy reflection signal (A‐scan) u(t) and an associated reference signal x(t), the algorithms first solve the system identification problem to produce an optimal least‐squares bandlimited estimate h(t) of the impulse response of the material under test. Next, an algorithm based upon the method of alternating orthogonal projections produ...