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Publications Influence

Ten Lectures on Wavelets

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

TLDR

14,627 934- PDF

Continuous and Discrete Wavelet Transforms

TLDR

1,044 42- PDF

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

TLDR

443 33- PDF

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

145 15- PDF

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

163 13- PDF

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

71 11

Approximation by translates of refinable functions

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

170 9

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

184 9- PDF

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

71 9- PDF

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

98 7- PDF