Fast Geometric Algorithms for Tomographic Nondestructive Evaluation

In this paper we describe the development and application of a novel approach to fast nondestructive evaluation (NDE) via direct estimation of signi cant features from tomographic data without image reconstruction. Classically, the term tomographic has been used to refer only to X-ray, and perhaps magnetic resonance techniques, but in our framework we point out that it has been recently shown that synthetic aperture radar (SAR), ultrasound, and laser radar measurements can all be interpreted in terms of tomographic projections. Hence, the algorithms described in this paper will be widely applicable to a variety of modalities used for the inspection of civil structures. In numerous situations of practical interest, such as the inspection of large civil structures, a full set of data with high signal-to-noise ratio is usually di cult, if not impossible, to obtain due to physical and sensor contraints. Therefore, the accurate reconstruction of an image of the medium is often di cult. Hence, much research work to date has been concentrated on improving image reconstruction for NDE applications. Yet, in most NDE applications, the reconstructed image is not the nal product of interest. Instead, it is of interest to know whether a particular geometric feature (be it an anomalous crack or other object of interest) is present, and if so, to obtain a rough estimate of its shape and size. That is to say, a pixel-by-pixel reconstruction of the image is often unneccesary. Our proposed method, based on a fundamental property of the (projection) Radon transform, is aimed at directly extracting geometric features from a set of given noisy, and possibly sparse data, without pixel-by-pixel image reconstruction. The propose method eliminates the need for full image reconstruction in arriving at the image features, hence resulting in signi cantly fewer overall computations. In addition, this approach allows us to compute easily the statistics for the estimated features, therefore resulting in easily quanti able performance characteristics of the approach. Several important advantages inherent to our proposed approach include 1) real-time processing, 2) process automation, and 3) improved performance. In this paper we will present examples of these advantages and point out possible extensions and generalizations of the proposed ideas.