Symbolic-numeric sparse interpolation of multivariate polynomials
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Symbolic-numeric sparse interpolation of multivariate polynomials
Journal of Symbolic Computation
IEEE Transactions on Image Processing
Sampling piecewise sinusoidal signals with finite rate of innovation methods
IEEE Transactions on Signal Processing
Strongly concave star-shaped contour characterization by algebra tools
Signal Processing
Software for weighted structured low-rank approximation
Journal of Computational and Applied Mathematics
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We establish a set of results showing that the vertices of any simply connected planar polygonal region can be reconstructed from a finite number of its complex moments. These results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory, where in the former, it is of interest to estimate the shape of an object from a finite number of its projections, whereas in the latter, the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points. We show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem, and taking advantage of this relationship, we derive and illustrate several new algorithms for the reconstruction of the vertices of simply connected polygons from moments