Publications related to From Differential Equations to the Construction of New Wavelet-Like Bases

Cryptanalysis of reduced-round MIBS Block cipher

Serge Vaudenay, Jorge Nakahara, Asli Bay

This paper presents the first independent and systematic lin- ear, differential and impossible-differential (ID) cryptanalyses of MIBS, a lightweight block cipher aimed at constrained devices such as RFID tags and sensor networks. Our contributions include ...

Springer2010

Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

Charles Stuart, Hicham Georges Gebran

We consider second-order quasilinear elliptic systems on un-bounded domains in the setting of Sobolev spaces. We complete our earlier work on the Fredholm and properness properties of the associated differential operators by giving verifiable conditions fo ...

2010

A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology

Ricardo Esteban Ruiz Baier

The bidomain model of electrical activity of myocardial tissue consists of a possibly degenerate parabolic PDE coupled with an elliptic PDE for the transmembrane and extracellular potentials, respectively. This system of two scalar PDEs is supplemented by ...

Wiley-Blackwell2010

Operator-like wavelets with application to functional magnetic resonance imaging

Ildar Khalidov

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smo ...

EPFL2009

Fractional Laplacian Pyramids

Michaël Unser, Ricard Delgado Gonzalo, Pouya Dehghani Tafti

We provide an extension of the L-2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyha ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

Michaël Unser, Chandra Sekhar Seelamantula

This paper deals with the problem of time-resolved fluorescence diffuse optical tomography. We propose a new reconstruction scheme based on a multi-resolution approximation of the time-resolved signals. The underlying basis functions are exponential B-spli ...

IEEE2009

Shift-Invariant Spaces from Rotation-Covariant Functions

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

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage, Katarina Balac

The “Marr wavelet pyramid” is a wavelet decomposition that implements a multiscale version of the complex gradient-Laplace operator. It is closely linked to a multiresolution analysis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) and it has a fast filterbank im ...

EURASIP2008

The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single- ...

IEEE2008

From Differential Equations to the Construction of New Wavelet-Like Bases

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Cryptanalysis of reduced-round MIBS Block cipher

Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology

Operator-like wavelets with application to functional magnetic resonance imaging

Fractional Laplacian Pyramids

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

Shift-Invariant Spaces from Rotation-Covariant Functions

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The Marr Wavelet Pyramid

Cryptanalysis of reduced-round MIBS Block cipher

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

Operator-like wavelets with application to functional magnetic resonance imaging

Shift-Invariant Spaces from Rotation-Covariant Functions

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Marr Wavelet Pyramid

Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

Fractional Laplacian Pyramids