Multiresolutionanalyyysi
Multiresolutionanalyyysi is a mathematical framework used in harmonic analysis and signal processing to decompose functions into components at different scales; in English-language literature it is typically called multiresolution analysis (MRA).
An MRA consists of a nested sequence of closed subspaces V_j of L^2(R) such that V_j ⊂ V_{j+1},
There exist detail spaces W_j defined by V_{j+1} = V_j ⊕ W_j, and the mother wavelet ψ spans W_0,
In practice, multiresolution analysis leads to wavelet representations and efficient algorithms for the discrete wavelet transform
Historically, MRA was developed in the 1980s and 1990s by Stéphane Mallat and Yves Meyer, providing a
Beyond one dimension, multiresolution analysis extends to higher dimensions and various domains, enabling scalable representations in