Sparse convolution-based digital derivatives (TCS paper)

Our paper on 1D integer only numerical analysis has been published as: Henri-Alex Esbelin, Rémy Malgouyres, Sparse convolution-based digital derivatives, fast estimation for noisy signals and approximation results, Journal of Theoretical Computer Science (TCS), Elsevier, 2016. Summary:
  1. Notion of a Digital Derivative and main properties
  2. Different families of masks
  3. Multigrid convergence for derivative estimation for any order and from possibly noisy signal
  4. Explicit expression of uniform B-splines as piecewise Bernstein polynomials
  5. Multidiemensional Generalized B-Spline families, analytical functions, and piecewise Besier surfaces
  6. Interpretation of Digital Derivatives as derivatives of B-splines
The PDF of the paper available here