Enhancement of TEM Data and Noise Characterization by Principal Component Analysis
Techniques are needed to reduce the presence of random noise in transient electromagnetic (TEM) data and to reduce the influence of correlated noise from a wide variety of sources on automatic anomaly-picking routines for more accurate unexploded ordnance (UXO) detection with fewer false anomalies. The objective of this SERDP Exploratory Development (SEED) project was to develop a practical algorithm that enhances the signal in TEM data for UXO applications.
The premise of this project is the theoretical understanding and algorithm development of principal component analysis (PCA) as a de-noising and signal-separation tool for TEM data. PCA is a technique for simplifying a data set by reducing multidimensional data sets to lower dimensions for analysis. PCA is an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. By properly analyzing the various components, one can isolate the individual correlated signals not associated with the UXO and remove those components from the TEM data. In an ideal case, this leaves only the signal from UXO and UXO-like anomalies, eliminating completely any error in the signal caused by external noise.
The project team developed a PCA algorithm tailored to UXO applications. Decay characteristics of TEM data preclude the standard Karhunen-Loeve transform, and the team addressed these issues with algorithm modifications, which were incorporated into the workflow.
The team then identified the optimum choice of principal components for the attenuation of both random noise and correlated noise, leaving the signal due to UXO intact. The team showed that the processed data is optimally prepared for automatic anomaly picking routines with a reduced number of false anomalies. The team demonstrated this on both synthetic examples of UXO surveys, as well as on TEM data from Kaho'olawe, Hawaii.
Finally, the team identified a critical issue with inversion of processed data that results in inaccurate recovered models without the incorporation of the PCA process into the forward model. The team developed an inversion algorithm that takes the processing steps into account during construction of the inverse kernels, leading to more accurate recovered models of inverted anomalies.
Not only does PCA have the ability to remove uncorrelated noise, it also can decompose a signal into sources from its constituent components. Although PCA methods vary in their application, they all are similar in that they deconstruct a multichannel signal into a set of orthogonal bases of decreasing energy. These sets can be reconstructed into the original signal exactly, or a truncated series can be reconstructed that will be minimally affected by noise uncorrelated with the desired UXO signal. Effective separation of noise components from field TEM data will contribute to improving UXO detection in difficult geologic environments and enhancing TEM data for discrimination purposes.
Points of Contact
Dr. Yaoguo Li
Colorado School of Mines
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