Abstract
A mathematical framework for data representation and for noise reduction is presented in this paper. The basis of the approach lies in the use of wavelets derived from the general theory of frames to construct a subspace capable of representing the original signal excluding the noise. The representation subspace is shown to be efficient in signal modeling and noise reduction, but it may be accompanied by an ill-conditioned inverse problem.
This is further examined, and a more adequate orthonormal representation for the generated subspace is proposed with an improvement in compression performance.
| Original language | English |
|---|---|
| Pages (from-to) | 587-597 |
| Number of pages | 11 |
| Journal | IEEE Transactions on Signal Processing |
| Volume | 46 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Mar 1998 |
Bibliographical note
©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."Keywords
- data compression
- interference suppression
- inverse problems
- noise
- signal representation
- wavelet transforms
- data representation
- frame-based wavelets
- general theory of frames
- ill-conditioned inverse problem
- noise reduction
- orthonormal representation
- representation subspace
- signal modeling
- subspace
- wavelets