Publications related to Operator-like wavelets with application to functional magnetic resonance imaging

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

Recursive analysis of singular ordinary differential equations

We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the ...

Elsevier2010

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

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

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

Adjoint Sensitivity Analysis of Index-One Multistage Differential Equations

Dominique Bonvin, Benoît Chachuat

Many practical chemical engineering processes involve a sequence of distinct transient operations, forming multistage systems in which each stage is described by mixed sets of differential and algebraic equations (DAEs). These models usually involve decisi ...

2007

Operator-like wavelets with application to functional magnetic resonance imaging

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Wavelet Steerability and the Higher-Order Riesz Transform

Recursive analysis of singular ordinary differential equations

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

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

Adjoint Sensitivity Analysis of Index-One Multistage Differential Equations

Wavelet Steerability and the Higher-Order Riesz Transform

Cryptanalysis of reduced-round MIBS Block cipher

Recursive analysis of singular ordinary differential equations

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

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

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

Adjoint Sensitivity Analysis of Index-One Multistage Differential Equations

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

The Marr Wavelet Pyramid

Shift-Invariant Spaces from Rotation-Covariant Functions