Abstract
Affine frames, generated by affine transform of one or several frame generator elements, can provide redundant but sparse representations of complex data. Such redundant feature guarantees the realization of robust data transmission through sparse reconstruction and noise suppression achieved at the same time. Frame tree is a tree-like connection among affine frame generators, each of which can provide a refined partition of some spatial-scale region linked with different branches in frame trees. The depth of frame trees, which determines how fine of spatial-scale cells in frame representation, may be finite or infinite. A suitable frame can be picked up fast from frame tree to mine complex data with abrupt changes only on small spatial-scale regions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zhang, Z., Jorgensen, P.E.T. (2024). Affine Frames. In: Frame Theory in Data Science. Advances in Science, Technology & Innovation. Springer, Cham. https://doi.org/10.1007/978-3-031-49483-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-031-49483-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-49482-6
Online ISBN: 978-3-031-49483-3
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)