ADAPTIVE NONLINEAR INVERSION ALGORITHMS

COMPUTATIONALLY EFFICIENT INVERSION ALGORITHMS ARE NEEDED IN A VARIETY OF DISCIPLINES, SUCH AS MEDICAL IMAGING, NONDESTRUCTIVE EVALUATION, GEOPHYSICAL PROSPECTING, AND ROBOTIC VISION. THE RIGOROUS MATHEMATICAL MODELS OF INVERSION THAT ARE ASSOCIATED WITH THESE PROBLEM AREAS ARE USUALLY NONLINEAR, BECAUSE THEY INVOLVE THE PRODUCT OF AN UNKNOWN MATERIAL PARAMETER (SUCH AS ELECTRICAL CONDUCTIVITY)AND AN UNKNOWN FIELD VECTOR. WE PROPOSE TO DEVELOP COMPUTATIONALLY EFFICIENT, ADAPTIVE ALGORITHMS FOR SUCH NONLINEAR PROBLEMS. WE WILL STUDY THE BASIC MATHEMATICAL MODEL FOR ELECTROMAGNETIC (EDDY-CURRENT) NONDESTRUCTIVE EVALUATION, BECAUSE THAT IS A PROBLEM AREA WITH WHICH WE AREQUITE FAMILIAR. THE TECHNIQUES, HOWEVER, CAN BE APPLIED TO ACOUSTIC INVERSION, OR ANY OF THE OTHER AREAS MENTIONED ABOVE. THIS RESEARCH EFFORT WILL EXTEND WORK DONE BY SABBAGH ASSOCIATES UNDER THREE EARLIER SBIR CONTRACTS, ONE WITH THE DEPARTMENT OF ENERGY, AND TWO WITH THE DEPARTMENT OF DEFENSE(NAVAIR, NAVAL SURFACE WEAPONS CENTER-WHITE OAK). THESE SBIR EFFORTS DEALT WITH MODELING AND THE DEVELOPMENT OF INVERSION ALGORITHMS FOR EDDY-CURRENT NONDESTRUCTIVE EVALUATION.