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Data compression with \(\Sigma\Pi\)-approximations based on splines. (English) Zbl 0792.65003
The authors describe a new \(\Sigma \Pi\)-algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. This algorithm based on continuous and discrete splines is used to compress the functions attached to red-green- blue colour images. Estimations of the compression coefficient are given.
Using the discrete splines for data compression the authors process images after scanning. Expert evaluation for some colour \(320\times 200\) images are given.
Reviewer: M.Gaşpar (Iaşi)
MSC:
65D07 Numerical computation using splines
68U10 Computing methodologies for image processing
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References:
[1] V. A. Vasilenko: The best finite dimensional \(\Sigma \Pi\)-approximation. Sov. J. Num. Anal. Math. Mod. 5 (1990), no. 4/5, 435-443. · Zbl 0816.65006
[2] W. A. Light E. W. Cheney: Approximation theory in tensor product spaces. Lectures Notes in Math., Springer Verlag, 1985. · Zbl 0575.41001 · doi:10.1007/BFb0075391
[3] C. DeBoor: A practical guide to splines. Appl. Math. Sci. 27 (1978).
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