Local average sampling and reconstruction with fundamental splines of fractional order

2019/04/06 by P. Devaraj, Devaraj, P., Peter Massopust +3
Engineering · Mathematics · Computer Science · #Advanced Numerical Analysis Techniques #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods

paper · pdf · doi:10.48550/arxiv.1904.03434

Abstract

We analyse sampling and average sampling techniques for fractional spline subspaces of L²(ℝ). Fractional B-splines β_σ are extensions of Schoenberg's polynomial splines of integral order to real order σ> -1. We present the interpolation with fundamental splines of fractional order for σ≥ 1 and the average sampling with fundamental splines of fractional order for σ≥ (3)/(2). Further, we generalise Kramer's lemma in the context of local average sampling.

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