Eddy current image restoration by constrained gradient descent

Abstract

We present in this paper an image restoration method for recovering the geometry of a flaw in a conducting surface from an eddy current image. Image restoration is formulated as a maximum likelihood estimation problem and is solved using constrained iterative gradient descent. A novel frequency-domain constraint relaxation algorithm is used to control the iterative restoration process. The technique is applied to eddy current images generated by sampling the output of an absolute transducer on a dense grid, creating smoothly blurred images of crack-like flaws. The following results were obtained: (1) Images of a range of sizes of electrical discharge machined (EDM) slots in the surface of a non-ferrous block that encompassed the transducer coil diameter were successfully restored. (2) Excellent results were also obtained for synthetic flaw images with very low signal-to-noise ratios. (3) Synthetic images of multiple flaws spaced less than a coil diameter apart were restored. (4) synthetic images of “V” and pit-shaped flaws were successfully restored. The principal conclusions drawn from this work are: (1) Representing a nonlinear system with layers of linear blurs and non-linear point transformations is general, permitting efficient gradient descent on any analytic system function. (2) Smooth blurring functions in the gradient improve the stability of the algorithm. (3) The accuracy of the estimate is improved dramatically by restoring portions of estimate spectrum which correspond to the highest signal-to-noise ratio band in the observation spectrum first.