05261277

j

05261277 Georgieva, Irina Uluchev, Rumen Smoothing of Radon projections type of data by bivariate polynomials. J. Comput. Appl. Math. 215, No. 1, 167-181 (2008). 2008 Elsevier Science B.V. (North-Holland), Amsterdam EN Reconstruction of bivariate polynomials Radon transform Chebyshev polynomials multivariate polynomials interpolation least squares approximation image processing

doi:10.1016/j.cam.2007.04.002

The authors study the problem of existence and uniqueness of reconstructing a bivariate polynomial $$P(x,y)= \sum_{i+j\leq n}\alpha_{i,j}x^{i}y^{j}$$ by the Radon projections along a set of chords of the unit disk. Chebyshev polynomials of the second kind and an interpolatory scheme for a mixed type of data play an important role in this problem. The article includes some numerical examples of reconstruction to illustrate the obtained results. Ivan Secrieru (Chi\c sin\u au)