Regularity of Refinable Function Vectors First draft (2009)
Albert Cohen, Ingrid Daubechies, Gerlind Plonka
1. Introduction In this paper we shall discuss the smoothness of refinable function vectors. These are solutions to functional equations of the type OE(x) =
08492 Executive Summary -- Structured Decompositions and Efficient Algorithms (2009)
Dahlke, Stephan, Daubechies, Ingrid, Elad, Michael, Kutyniok, Gitta, Teschke, Gerd
New emerging technologies such as high-precision sensors or new MRI machines drive us towards a challenging quest for new, more effective, and more daring mathematical models and algorithms....
08492 Abstracts Collection -- Structured Decompositions and Efficient Algorithms (2009)
Dahlke, Stephan, Daubechies, Ingrid, Elad, Michael, Kutyniok, Gitta, Teschke, Gerd
From 30.11. to 05.12.2008, the Dagstuhl Seminar 08492 ``Structured Decompositions and Efficient Algorithms '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar,...
Ingrid Daubechies, Konstantinos Drakakis, Tanya Khovanova
Abstract. The connectivity of the autonomous systems (ASs) in the Internet can be modeled as a time-evolving random graph, whose nodes represent ASs and whose edges represent direct connections...
16th International Congress on Mathematical Physics (2008)
Aizenman, Michael, Daubechies, Ingrid, Exner, Pavel, Froehlich, Juerg, Gallavotti, Giovanni, Sinai, Yakov, ...
Iteratively re-weighted least squares minimization for sparse recovery (2008)
Daubechies, Ingrid, DeVore, Ronald, Fornasier, Massimo, Gunturk, C. Sinan
We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We prove its convergence and we estimate its local rate....
Analysis of boosting algorithms using the smooth margin function (2008)
Rudin, Cynthia, Schapire, Robert E., Daubechies, Ingrid
We introduce a useful tool for analyzing boosting algorithms called the ``smooth margin function,'' a differentiable approximation of the usual margin for boosting algorithms. We present two boosting...
variational functionals (2008)
Ingrid Daubechies, Gerd Teschke, I. Daubechies A, G. Teschke B
We discuss a wavelet based treatment of variational problems arising in the context of image processing, inspired by papers of Vese–Osher and Osher–Solé–Vese, in particular, we introduce a...
variational functionals (2008)
Ingrid Daubechies, Gerd Teschke, I. Daubechies A, G. Teschke B
We discuss a wavelet based treatment of variational problems arising in the context of image processing, inspired by papers of Vese–Osher and Osher–Solé–Vese, in particular, we introduce a...
The canonical dual frame of a wavelet frame (2008)
In this note we show that there exist wavelet frames that have nice dual wavelet frames, but for which the canonical dual frame does not consist of wavelets, i.e., cannot be generated by the...
Cynthia Rudin, Ingrid Daubechies, Robert E. Schapire
In order to understand AdaBoost’s dynamics, especially its ability to maximize margins, we derive an associated simplified nonlinear iterated map and analyze its behavior in low-dimensional cases....
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald Devore
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is \almost " characterized...
Albert Cohen, Ingrid Daubechies, Amos Ron
) is called PSI (principal shift-invariant) if it is the smallest space that contains all the shifts (i.e., integer translates) of some function OE 2 L 2. Ideally, each function f in such PSI V can...
Pairs of Dual Wavelet Frames From Any Two Re nable Functions (2007)
Starting from any two compactly supported renable functions in L 2 (R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they...
Pairs of Dual Wavelet Frames From Any Two Re nable Functions (2007)
Starting from any two compactly supported renable functions with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a...
Ingrid Daubechies, Igor Guskov
Abstract. We present a generalization of Lemari'e's commutation formula to irregular subdivision schemes and wavelets. We show how in the non-interpolating case the divided differences need...
Sparse and stable Markowitz portfolios (2007)
Brodie, Joshua, Daubechies, Ingrid, De Mol, Christine, Giannone, Domenico, Loris, Ignace
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the...
2007/61 Sparse and Stable Markowitz Portfolios (2007)
Joshua Brodie, Ingrid Daubechies, Christine De Mol, Domenico Giannone
The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years. However, efforts to translate this theoretical foundation into a viable...
Tomographic inversion using $\ell_1$-norm regularization of wavelet coefficients (2006)
Loris, Ignace, Nolet, Guust, Daubechies, Ingrid, Dahlen, F. A.
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed...
Iteratively solving linear inverse problems under general convex constraints (2006)
Ingrid Daubechies, Gerd Teschke, Luminita Vese
Abstract. We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber...
Daubechies, Ingrid, Drakakis, Konstantinos, Khovanova, Tanya
The connectivity of the autonomous systems (ASs) in the Internet can be modeled as a time-evolving random graph, whose nodes represent ASs (or routers), and whose edges represent direct connections...
Zou, Jing, Gilbert, Anna, Strauss, Martin, Daubechies, Ingrid
We analyze a sublinear RAlSFA (Randomized Algorithm for Sparse Fourier Analysis) that finds a near-optimal B-term Sparse Representation R for a given discrete signal S of length N, in time and space...
The dynamics of adaboost: Cyclic behavior and convergence of margins (2004)
Cynthia Rudin, Ingrid Daubechies, Robert E. Schapire
In order to study the convergence properties of the AdaBoost algorithm, we reduce AdaBoost to a nonlinear iterated map and study the evolution of its weight vectors. This dynamical systems approach...
The dynamics of adaboost: Cyclic behavior and convergence of margins (2004)
Cynthia Rudin, Ingrid Daubechies, Robert E. Schapire, Dana Ron
In order to study the convergence properties of the AdaBoost algorithm, we reduce AdaBoost to a nonlinear iterated map and study the evolution of its weight vectors. This dynamical systems approach...
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint (2003)
Daubechies, Ingrid, Defrise, Michel, De Mol, Christine
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing...
Harmonic Analysis of the space BV (2003)
Cohen, Albert, Dahmen, Wolfgang, Daubechies, Ingrid, DeVore, Ronald
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is "almost" characterized by...
Harmonic analysis of the space BV (2003)
Daubechies, Ingrid, Cohen, Albert, Dahmen, Wolfgang, Vore, Ronald De
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is almost characterized by wavelet...
On the Dynamics of Boosting (2003)
Cynthia Rudin, Ingrid Daubechies, Robert E. Schapire
In order to understand AdaBoost's dynamics, especially its ability to maximize margins, we derive an associated simplified nonlinear iterated map and analyze its behavior in low-dimensional...
On the Importance of Combining Wavelet-based Nonlinear Approximation with Coding Strategies (2002)
Albert Cohen, Ingrid Daubechies, Onur Guleryuz, Michael Orchard
In theoretical models for the mathematical study of compression, signals and particularly images are often viewed as realizations of an (unknown) stochastic process. The corresponding Karhunen-Lo`eve...
On the Importance of Combining Wavelet-based Nonlinear Approximation with Coding Strategies (2002)
Albert Cohen, Ingrid Daubechies, Onur G. Guleryuz, Michael T. Orchard
This paper provides a mathematical analysis of transform compression in its relationship to linear and non-linear approximation theory. Contrasting linear and non-linear approximation spaces, we show...
Normal multiresolution approximation of curves (2002)
Ingrid Daubechies, Olof Runborg, Wim Sweldens
ABSTRACT. A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study...
Framelets: MRA-based constructions of wavelet frames (2001)
Ingrid Daubechies, Ingrid Daubechies, Bin Han, Bin Han, Amos Ron, Amos Ron, ...
We discuss wavelet frames constructed via multiresolution analysis (MRA), with emphasis on tight wavelet frames. In particular, we establish general principles and specific algorithms for...
Framelets: MRA-based constructions of wavelet frames (2001)
Ingrid Daubechies, Ingrid Daubechies, Bin Han, Bin Han, Amos Ron, Amos Ron, ...
We are interested here in wavelet frames and their construction via multiresolution analysis (MRA); of particular interest to us are tight wavelet frames. The redundant representation o#ered by...
Tree approximation and optimal encoding (2001)
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald Devore
Tree approximation is a new form of nonlinear approximation which appears naturally in some applications such as image processing and adaptive numerical methods. It is somewhat more restrictive than...
Harmonic Analysis of the space BV \Lambda (2001)
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald Devore
Abstract We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is "almost...
Harmonic analysis of the space BV (2000)
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald Devore
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is \almost " characterized...
The Canonical Dual Frame of a Wavelet Frame (2000)
Ingrid Daubechies Pacm, Ingrid Daubechies, Bin Han, Tg G
this paper, let's discuss it in full detail. Following [6], we denote L 00 (R) := ff 2L 2 (R) : b f 2 L1 (R) and b f() = 0 for all 62 f : 1=c 6 jj 6 cg for some constant c > 1g: (2.5) By...
Pairs of dual wavelet frames from any two refinable functions (2000)
Starting from any two compactly supported refinable functions in L2(R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they...
Pairs of dual wavelet frames from any two refinable functions (2000)
Research was partially supported by grants NSF (DMS-9872890, DMS-9706753) and AFOSR (F49620-98-1-
Harmonic analysis of the space BV (2000)
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald Devore
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is “almost ” characterized by...
Tree Approximation and Optimal Encoding (1999)
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald Devore
Tree approximation is a new form of nonlinear approximation which appears naturally in some applications such as image processing and adaptive numerical methods. It is somewhat more restrictive than...
Wavelets on Irregular Point Sets (1999)
Ingrid Daubechies, Igor Guskov, Peter Schröder, Wim Sweldens
this article we review techniques for building and analyzing wavelets on irregular point sets in one and two dimensions. We discuss current results both on the practical and theoretical side. In...
Wavelets on Irregular Point Sets (1999)
Ingrid Daubechies, Igor Guskov, Peter Schröder, Wim Sweldens
In this article we review techniques for building and analyzing wavelets on irregular point sets in one and two dimensions. We discuss current results both on the practical and theoretical side. In...
Tree Approximation and Encoding (1999)
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald Devore
Tree approximation is a new form of nonlinear approximation which appears naturally in some applications such as image processing and adaptive numerical methods. It is somewhat more restrictive than...
Tools for Time-Frequency Analysis (1998)
Together with students and postdocs, the PI has worked on the mathematical aspects and applications of various tools in time frequency or time scale analysis. they have brought a deeper understanding...
Data compression and harmonic analysis (1998)
Donoho, David L., Vetterli, Martin, DeVore, R. A., Daubechies, Ingrid
Data compression and harmonic analysis (1998)
David L. Donoho, Martin Vetterli, R. A. Devore, Ingrid Daubechies
In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon’s R(D) theory...
Factoring wavelet transforms into lifting steps (1998)
Ingrid Daubechies, Wim Sweldens
ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple...
Regularity Of Irregular Subdivision (1998)
Ingrid Daubechies, Igor Guskov, Wim Sweldens
. We study the smoothness of the limit function for one dimensional unequally spaced interpolating subdivision schemes. The new grid points introduced at every level can lie in irregularly spaced...
On the Importance of Combining Wavelet-Based Non-Linear Approximation With Coding Strategies (1997)
Albert Cohen Ingrid, Albert Cohen, Ingrid Daubechies, Onur Guleryuz, Michael Orchard
this paper is to provide with such a mathematical analysis.
Regularity of re nable function vectors (1997)
Albert Cohen, Ingrid Daubechies, Gerlind Plonka
We study the existence and regularity of compactly supported solutions = ( ) r;1 =0 of vector re nement equations. The space spanned by the translates of can only provide approximation order if the...
A new technique to estimate the regularity of refinable functions (1996)
Daubechies, Ingrid, Cohen, Albert
We study the regularity of refinable functions by analyzing the spectral properties of special operators associated to the refinement equation; in particular, we use the Fredholm determinant theory...
Non-separable bidimensional wavelets bases. (1993)
Cohen, Albert, Daubechies, Ingrid
We build orthonormal and biorthogonal wavelet bases of L2(R2) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a...
Ten Lectures on Wavelets (1992)
Contenido: El qué, por qué y cómo de la ondículas (wavelets); La transformación continua de las ondículas; Transformación discreta de ondículas: marcos; Densidad de frecuencia-tiempo y bases...
Thesis (doctoral)--Vrije Universiteit Brussel, 1979-1980.
Diederik Aerts, Ingrid Daubechies
We require the following three conditions to hold on two systems being described as a joint system: (1) the structure of the two systems is preserved: (2) a measurement on one of the systems does not...
Sparse and Stable Markowitz Portfolios
Brodie, Joshua, Daubechies, Ingrid, De Mol, Christine, Giannone, Domenico
The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years. However, efforts to translate this theoretical foundation into a viable...
Sparse and stable Markowitz portfolios.
Joshua Brodie, Ingrid Daubechies, Christine De Mol, Domenico Giannone, Ignace Loris
We consider the problem of portfolio selection within the classical Markowitz meanvariance optimizing framework, which has served as the basis for modern portfolio theory for more than 50 years....
Regularity of Refinable Function Vectors
Albert Cohen, Ingrid Daubechies, Gerlind Plonka
this paper we shall discuss the smoothness of refinable function vectors. These are solutions to functional equations of the type
Sparse and stable Markowitz portfolios
Joshua Brodie, Ingrid Daubechies, Christine De Mol, Domenico Giannone, Ignace Loris
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the...