Multiresolution Analysis

Mallat's MRA framework and orthonormal wavelet bases.

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Multiresolution Analysis. Mallat’s MRA framework and orthonormal wavelet bases.

Foundations and canonical references

The standard treatments of multiresolution analysis approach the subject from complementary angles. Daubechies, Ten Lectures on Wavelets (1992) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Mallat, A Wavelet Tour of Signal Processing (2008) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for multiresolution analysis include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 1992
    Ten Lectures on Wavelets
    daubechies-1992
  • textbook · primary · 2008
    A Wavelet Tour of Signal Processing
    mallat-2008

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