Tomographic Reconstruction of Polygons from Knot Location and Chord Length Measurements

projection and Fourier methods [1, 2] are used to reconstruct high resolution images in a variety of applications In this work, we develop statistically based algorithms to reconstruct binary polygonal objects from sparse and noisy [1]. Although these methods produce high quality images, tomographic-based observation data. Traditional approaches they require a large number of projections and a relatively to the reconstruction of geometric objects from projection data high signal-to-noise ratio (SNR). In applications where often lead to highly nonlinear estimation problems. To avoid number, spacing, or SNR of the projections are severely the difficulties associated with such nonlinear problems, we constrained a high resolution image is virtually impossible. first examine the problem of reconstruction of an object based In this paper, we develop algorithms that utilize a priori on knot location measurements, i.e., measurements of the locaknowledge about the nature of underlying object to extract tions of abrupt change in the projections. The ties between this geometric information from sparse and noisy projection problem and that of multitarget radar tracking enable us to measurements. This approach follows from work in geodevelop a sequential hypothesis-testing algorithm requiring metric-based algorithms [3–8] which develop parametric only the solution of a series of linear estimation problems. In reconstruction algorithms to obtain geometric information particular, data association hypotheses are generated, under from data. The primary objective of these approaches is each of which the inversion is linear. The complexity of the to achieve focusing of the information in sparse and noisy association possibilities are kept in check through the use of constraints on the reconstruction imposed by the tomography data to directly determine the shape of the underlying problem. The solution of this first problem is then used as an object, rather than reconstructing all of the pixels of the initialization to a more complete reconstruction which, while associated image. In this spirit, we assume that the underutilizing all the projection data, is nonlinear. We demonstrate lying object is a binary polygon and estimate the 2Nv pathat the estimates provided by the first, efficient algorithm are rameters that define the Nv vertices of the polygon. Thus, of good quality on their own, and, when combined with a fully the sparse data are focused on the parameters that are nonlinear inversion, produce excellent object estimates.  1996 instrumental to the reconstruction of the object. Academic Press, Inc. For a binary object, the projection data are a collection of projected thickness or chord length measurements of the object. The reconstruction of the vertices of a binary