Maximum Likelihood Estimation of A-Scan Amplitudes for Coherent Targets in Media of Unresolvable Scatterers

The paper derives maximum likelihood estimator (MLE) for A-scan amplitudes corresponding to coherent reflectors embedded in media of unresolvable scatterers. The MLE processes sampled RF A-scans from broadband ultrasonic pulse-echo systems. A major source of interference for these signals is the back scattered energy from the unresolvable scatterers that exist throughout the beam field. A statistical model is formulated that characterizes the back scattered energy from a resolution cell when a coherent target scatterer is present. The backscattered energy from the interfering scatterers is modeled by complex random variables corresponding to the discrete Fourier coefficients of the sampled resolution cell. It is shown that the MLE is equivalent to a matched filter when the distribution of the interfering back scatter energy is stationary over the resolution cell. In addition, the form of the MLE is described when the interfering echoes are not stationary within the resolution cell. Experimental results are presented for an adaptive implementation of the MLE applied to flaw detection in stainless steel. The results demonstrate the ability of the MLE to reveal targets masked by grain echoes, without a priori knowledge of the grain-echo spectral characteristics.