A Theory for Multiresolution Signal Decomposition

Mallat, S. G. (1989). A Theory for Multiresolution Signal Decomposition: The Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674-693.

Type

Journal article

Intellectual base

Primary research

Year

1989

Volume

11

Issue

7

Pages

674-693

DOI

10.1109/34.192463

DOI registrant

Institute of Electrical and Electronics Engineers

Link

https://doi.org/10.1109/34.192463

Cited by

2 citations across 2 artifacts.

Domain-specific

• Discrete wavelet transform
  • A one-level critically sampled DWT maps a sequence (x[k]) to approximation coefficients \(a_1[n]=\sum_k h[k-2n]x[k]\) and detail coefficients \(d_1[n]=\sum_k g[k-2n]x[k]\), with further levels recursively decomposing the approximation branch under the selected convention.
• Multiresolution Analysis
  • Mallat's formulation showed how this nested approximation structure yields orthogonal wavelets and a pyramidal filter-bank algorithm.

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