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Smoothing of Radon projections type of data by bivariate polynomials. (English) Zbl 1144.65080

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.

MSC:

65R10 Numerical methods for integral transforms
65D05 Numerical interpolation
44A12 Radon transform
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65D10 Numerical smoothing, curve fitting
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