Multiscale geometric analysis
Encyclopedia
Multiscale geometric analysis or geometric multiscale analysis is an emerging area of high-dimensional signal processing
and data analysis
.
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
and data analysis
Data analysis
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making...
.
See also
- WaveletWaveletA wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...
- Scale spaceScale spaceScale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision...
- Multi-scale approachesMulti-scale approachesThe scale-space representation of a signal obtained by Gaussian smoothing satisfies a number of special properties, scale-space axioms, which make it into a special form of multi-scale representation. There are, however, also other types of multi-scale approaches in the areas of computer vision,...
- Multiresolution analysisMultiresolution analysisA multiresolution analysis or multiscale approximation is the design method of most of the practically relevant discrete wavelet transforms and the justification for the algorithm of the fast wavelet transform...
- Singular value decompositionSingular value decompositionIn linear algebra, the singular value decomposition is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics....
- Compressed sensingCompressed sensingCompressed sensing, also known as compressive sensing, compressive sampling and sparse sampling, is a technique for finding sparse solutions to underdetermined linear systems...
Further reading
- Multiscale Geometry and Analysis in High Dimensions
- Emerging applications of geometric multiscale analysis
- Near-Optimal Detection of Geometric Objects by Fast Multiscale Methods, Ery Arias-Castro, David DonohoDavid DonohoDavid Leigh Donoho, born on March 5, 1957 in Los Angeles, is a professor of statistics at Stanford University, where he is also the Anne T. and Robert M. Bass Professor in the Humanities and Sciences...
, Xiaoming Huo - Analysis of the Spatial Distribution of Galaxies by Multiscale Methods, J-L. Starck, V. J. Martınez, D. L. DonohoDavid DonohoDavid Leigh Donoho, born on March 5, 1957 in Los Angeles, is a professor of statistics at Stanford University, where he is also the Anne T. and Robert M. Bass Professor in the Humanities and Sciences...
, O. Levi, P. Querre, E. Saar