| Three methods of object recognition using wideband electromagnetic induction data are described. A fourth method, which extends an existing algorithm to extract features using a dictionary based search, was developed to analyze objects. Emphasis was given to speed of execution as our interest is in their real-time performance.;Wideband electromagnetic induction data may consist of a wide range of frequencies starting from a few Hz to a few hundred thousand Hz. In addition to the object, the data usually has information about the sensor geometry, orientation of data collection setup and the medium in which the object lies.;The first method is called the Prototype Angle Matching (PRAM) algorithm that takes a non-parametric approach using the gradient angle between the real and imaginary components of the data. It classifies using distance from prototypes whose gradient angles have been measured. It is fast and does not make any assumptions about the data.;The second method, the Gradient Angle Model Algorithm (GRANMA), is based on a novel analytical derivation of the gradient angle using a first order Cole-Cole model. The analytical derivation reduces the number of parameters from four to two, enabling a fast look-up approach to nearest-neighbor classification schemes. Furthermore, the other two parameters can easily be estimated from the first two. The method is demonstrated to be much faster and more robust than existing methods.;The third method, Gradient Angles in Parts Algorithm (GRANPA) uses a piecewise Cole-Cole modeling approach to attempt to estimate parameters of higher order models. It estimates the frequency segments in the data that follow the Cole-Cole model in an automated way and then uses the same setup as the GRANMA to extract the parameters.;The fourth set of methods, collectively referred to as SPARse DIelectric Relaxation estimation (SPARDIR), use a model that generalizes the Discrete Spectrum of Relaxation Frequencies (DSRF) model. The SPARDIR algorithms assume that the data are formed by a weighted combination of the Cole-Cole models and use a gradient Newton framework to search for parameters. A variety of combinations of L1 and L2 norm-based objective functions and constraints are investigated to seek sparse, physically meaningful parameter estimates. Furthermore, SPARDIR algorithms are devised that perform joint sparse estimation of parameters over a set of measurements and compared to SPARDIR and DSRF algorithms that perform point-wise sparse estimation.;Classification and parameter estimation results are given on sets of real, measured data as well as synthetic data sets for which the true parameter values are known. In these experiments, GRANMA performed better, more robust and with higher classification rates, than several existing algorithms and is faster than all but one. The Joint SPARDIR algorithms more accurately estimated the true underlying model parameters for more general models than previous work. In addition, the Joint SPARDIR algorithms are general; they are not specific to sensor type. |
