Defect detection in correlated noise
Nondestructive evaluation (NDE) has been extensively used for investigating the integrity of materials and characterizing cracks or defects. We present methods for detecting NDE defect signals in correlated noise having unknown covariance. The proposed detectors are derived using the statistical theory of generalized likelihood ratio (GLR) tests and multivariate analysis of variance (MANOVA). We consider both real and complex data models for data sets obtained from multiple experiments. To allow accurate estimation of the noise covariance, we incorporate secondary data containing only noise into the detector design. Probability distributions of the GLR test statistics are derived under the null hypothesis, i.e. assuming that the signal is absent, and used for the detector design. We also develop a numerical method for computing the exact decision threshold that guarantees a specified probability of false alarms. We apply the proposed methods to simulated and experimental data and demonstrate their superior performance compared with the detectors that neglect noise correlation.