C. Heil

Publications
Influence

I. Daubechies, C. Heil
Mathematics, Computer Science
1 May 1992

Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal wavelet bases of compactly supported wavelets and multiresolutional analysis. Expand

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Continuous and Discrete Wavelet Transforms

C. Heil, D. Walnut
Mathematics, Computer Science
SIAM Rev.
1 December 1989

This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ in terms of coherent states. Expand

1,044
42
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The application of multiwavelet filterbanks to image processing

V. Strela, P. N. Heller, G. Strang, P. Topiwala, C. Heil
Mathematics, Computer Science
IEEE Trans. Image Process.
1 April 1999

Multiwavelets are a new addition to the body of wavelet theory. Expand

Density, overcompleteness, and localization of frames

R. Balan, Peter G. Casazza, C. Heil, Zeph Landau
Mathematics
7 July 2006

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and… Expand

THE APPLICATION OF MULTIWAVELET FILTER BANKS TO IMAGE PROCESSING ∗

V. Strela, P. N. Heller, G. Strang, P. Topiwala, C. Heil
1995

Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filter banks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short… Expand

Matrix Refinement Equations: Existence and Uniqueness

C. Heil, D. Colella
Mathematics
1996

Matrix reenement equations are functional equations of the form f(x) = P N k=0 c k f(2x ? k), where the coeecients c k are matrices and f is a vector-valued function. Reenement equations play key… Expand

Approximation by translates of refinable functions

C. Heil, G. Strang, V. Strela
Mathematics
1 March 1996

Summary. The functions $f_1(x), \dots, f_r(x)$ are refinable if they are combinations of the rescaled and translated functions $f_i(2x-k)$ . This is very common in scientific computing on a regular… Expand

Modulation spaces and pseudodifferential operators

K. Gröchenig, C. Heil
Mathematics
1 December 1999

We use methods from time-frequency analysis to study boundedness and traceclass properties of pseudodifferential operators. As natural symbol classes, we use the modulation spaces onR2d, which… Expand

Linear independence of time-frequency translates

C. Heil, Jayakumar Ramanathan, P. Topiwala
Mathematics
1996

Abstract. The refinement equation φ(t) = ∑N2 k=N1 ck φ(2t − k) plays a key role in wavelet theory and in subdivision schemes in approximation theory. Viewed as an expression of linear dependence… Expand

Accuracy of Lattice Translates of Several Multidimensional Refinable Functions

C. Cabrelli, C. Heil, U. Molter
Mathematics
1 October 1998

Complex-valued functionsf1,?,fronRdarerefinableif they are linear combinations of finitely many of the rescaled and translated functionsfi(Ax?k), where the translateskare taken along a… Expand

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