A moment-based variational approach to tomographic reconstruction

Caption title.Includes bibliographical references (p. 24-26).Supported by the National Science Foundation. 9015281-MIP Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the US Army Research Office. DAAL03-92-G-0115 Supported by the Clement Vaturi Fellowship in Biomedical Imaging Sciences at MIT.Peyman Milanfar, W. Clem Karl, Alan S. Willsky

On the shape-from-moments problem and recovering edges from noisy Radon data

We consider the problem of reconstructing a planar convex set from noisy observations of its moments. An estimation method based on pointwise recovering of the support function of the set is developed. We study intrinsic accuracy limitations in the shape-from-moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error. It is shown that the proposed estimator is near-optimal in the sense of the order. An application to tomographic reconstruction is discussed, and it is indicated how the proposed estimation method can be used for recovering edges from noisy Radon data

Application of the Least Squares Solutions in Image Deblurring

A new method for the reconstruction of blurred digital images damaged by separable motion blur is established. The main attribute of the method is based on multiple applications of the least squares solutions of certain matrix equations which define the separable motion blur in conjunction with known image deconvolution techniques. The key feature of the proposed algorithms is reflected in the fact that they can be used only in symbiosis with other image restoration algorithms

Reconstructing polygons from moments with connections to array processing

Caption title.Includes bibliographical references (p. 24-26).Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the US Army Research Office. DAAL03-92-G-0115 Supported by the National Science Foundation. MIP-9015281 Supported by the Clement Vaturi Fellowship in Biomedical Imaging Sciences at MIT.Peyman Milanfar ... [et al.]