From Differential Equations to the Construction of New Wavelet-Like Bases
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We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is ...
Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007
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 ...
The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus. Among other properties, we show that they are the convolution kernels that link the ...
We consider a large class of quasilinear second order elliptic systems of the form - ∑α,β=1N aαβ(x,u(x)),∇u(x))∂2αβu(x) + b(x,u(x),∇u(x)) = 0, where x varies in an unbounded domain Ω of the Euclidean space RN and u = (u1,...,um) is a vector of functi ...
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 ...
The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...
In this paper, we consider the statistical decision processes behind a linear and a differential cryptanalysis. By applying techniques and concepts of statistical hypothesis testing, we describe precisely the shape of optimal linear and differential distin ...
In this paper, we consider the statistical decision processes behind a linear and a differential cryptanalysis. By applying techniques and concepts of statistical hypothesis testing, we describe precisely the shape of optimal linear and differential distin ...
Let f be an integrable function on RN, a a point in RN and B a complex number. If the mean value of f on the sphere of centre a and radius r tends to B when r tends to 0, we show that the Fourier integral at a of f is summable to B in Cesàro means of order ...
We build wavelet-like functions based on a parametrized family of pseudo-differential operators Lv that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...
