Dimension Reduction and Remote Sensing Using Modern Harmonic Analysis

John J. Benedetto () and Wojciech Czaja
Additional contact information
John J. Benedetto: University of Maryland, Norbert Wiener Center, Department of Mathematics
Wojciech Czaja: University of Maryland, Norbert Wiener Center, Department of Mathematics

A chapter in Handbook of Geomathematics, 2015, pp 2609-2632 from Springer

Abstract: Abstract Harmonic analysis has interleaved creatively and productively with remote sensing to address effectively some of the most difficult dimension reduction problems of modern times. These problems are part and parcel of fundamental ideas in machine learning and data mining, dealing with a host of data collection and data fusion technologies. Linear dimension reduction methods are the starting point herein, which themselves lead to the formulation of non-linear dimension reduction algorithms necessary to resolve information preserving dimension reduction associated with the likes of hyperspectral imagery and LIDAR data. Harmonic analysis arises in the form of data dependent non-linear kernel eigenmap methods, and it is fundamental to design and optimize techniques such as Laplacian and Schroedinger eigenmaps. These are exposited. Further, the fundamental roles in remote sensing of the theories of frames, compressed sensing, sparse representations, and diffusion-based image processing are explained. Significant examples and major applications are described.

Keywords: Sparse Representation; Compress Sense; Tight Frame; Dual Frame; Random Projection (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-54551-1_50

Ordering information: This item can be ordered from
http://www.springer.com/9783642545511

DOI: 10.1007/978-3-642-54551-1_50

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().