Fractional Splines and Wavelets

By Michael A. Unser, Thierry Blu. SIAM Review, 2000

344 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/3b729ca0b0ee23148a7507f45ef34ffa4ae023a8

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In Applied Mathematics

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Solving inverse problems using data-driven models (2019, unknown): “…at 15:29:08, subject to the Cambridge Core terms of use, available at Finally, in applied harmonic analysis, `p-norms of wavelets have been proposed as regularizers (Daubechies et al. 1991, Mallat 2009, Unser and Blu 2000, Kutyniok and Labate 2012, Eldar and Kutyniok 2012, Foucart and Rauhut 2013).”
Algorithms for the fractional calculus: A selection of numerical methods (2005, background): “... described, e.g., in the works of Chern [6] (finite element implementation of viscoelastic model), Diethelm and Freed [11] (viscoplastic material model), Gaul et al. [19] (description of mechanical systems subject to damping), G16ckle and Nonnenmacher [20] (relaxation and reaction kinetics of pol”
Finite Discrete Gabor Analysis (2007, methodology): “They have been developed by Unser and Blu in a series of papers [101, 12, 13] mostly in the context of wavelets and fractional Brownian motion.”
Fractional-Order Anisotropic Diffusion for Image Denoising (2007, methodology): “The fractional derivative has been applied to many fields such as noise detection and estimation [23], [24], electromagnetic theory [25], wavelets, and splines [26], [27].”
Fast parametric elastic image registration (2003, methodology): “We use orthonormal symmetric fractional B-spline wavelets [61], [62] of degree , which have precisely the desired regularity and Fourier decay at infinity.”
Sampling-50 years after Shannon (2000, background): “Examples of admissible generating functions, which are not covered by the Strang–Fix theory, are the fractional B-splines of degree ; these satisfy the partition of unity but have a fractional order of approximation [134].”
WSPM: Wavelet-based statistical parametric mapping (2007, methodology): “In this study, we opted for the orthogonal B-spline wavelet of degree 1.0 (Battle, 1987; Unser and Blu, 2000 ).”
Denoising functional MR images: a comparison of wavelet denoising and Gaussian smoothing (2004, methodology): “have proposed an FWT that uses fractional spline wavelets [27], [28].”
A survey on the magnetic resonance image denoising methods (2014, background): “have proposed the fast wavelet transform that uses fractional spline wavelets [64,65].”