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Explicit evaluation of the equivalent degrees of freedom of smoothing splines: A spectral factorization approach

Publications associées (62)

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The influence of regulatory uncertainty on investments

Bastian Wolfgang Schwark

Understanding firm reactions to regulatory uncertainty is vital for the functioning of a market. Deficient investments, particularly in the power generation sector, could jeopardize the market in the long run. ...

2009

Consistent And Regularized Magnification Of Images

Michaël Unser, Philippe Thévenaz, Aurélien Bourquard, Katarina Balac

Because more output data must be created than is available from the input, magnification is an III-posed problem. Traditional magnification relies on resampling an interpolation model at the appropriate rate; unfortunately, this simple solution is blind to ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Self-Similarity: Part I—Splines and Operators

Michaël Unser, Thierry Blu

The central theme of this pair of papers (Parts I and II in this issue) is self-similarity, which is used as a bridge for connecting splines and fractals. The first part of the investigation is deterministic, and the context is that of L-splines; these are ...

IEEE2007

Complex B-Splines

Michaël Unser, Thierry Blu

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated po ...

Elsevier2006

Polyharmonic Smoothing Splines and the Multidimensional Wiener Filtering of Fractal-Like Signals

Michaël Unser, Dimitri Nestor Alice Van De Ville

Motivated by the fractal-like behavior of natural images, we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional was initially introduced by Duchon for the approximatio ...

IEEE2006

Generalized Smoothing Splines and the Optimal Discretization of the Wiener Filter

Michaël Unser, Thierry Blu

We introduce an extended class of cardinal LL-splines, where L is a pseudo-differential operator satisfying some admissibility conditions. We show that the LL-spline signal interpolation problem is well posed and that its solution is the unique minimizer ...

IEEE2005

Green-Ampt approximations

David Andrew Barry

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of a ...

2005

Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms

Michaël Unser, Thierry Blu

Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the ...

IEEE2005

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Michaël Unser, Thierry Blu

ICIP'05 Best Student Paper Award We investigate the use of quasi-interpolating approximation schemes, to construct an estimate of an unknown function from its given discrete samples. We show theoretically and with practical experiments that such methods pe ...

IEEE2005

Recursive Filtering for Splines on Hexagonal Lattices

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

Hex-splines are a novel family of bivariate splines, which are well suited to handle hexagonally sampled data. Similar to classical 1D B-splines, the spline coefficients need to be computed by a prefilter. Unfortunately, the elegant implementation of this ...

IEEE2003