27 September 2011 Analysis of data separation and recovery problems using clustered sparsity
Author Affiliations +
Proceedings Volume 8138, Wavelets and Sparsity XIV; 813818 (2011); doi: 10.1117/12.892723
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States
Abstract
Data often have two or more fundamental components, like cartoon-like and textured elements in images; point, filament, and sheet clusters in astronomical data; and tonal and transient layers in audio signals. For many applications, separating these components is of interest. Another issue in data analysis is that of incomplete data, for example a photograph with scratches or seismic data collected with fewer than necessary sensors. There exists a unified approach to solving these problems which is minimizing the ℓ1 norm of the analysis coefficients with respect to particular frame(s). This approach using the concept of clustered sparsity leads to similar theoretical bounds and results, which are presented here. Furthermore, necessary conditions for the frames to lead to sufficiently good solutions are also shown.
© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Emily J. King, Gitta Kutyniok, Xiaosheng Zhuang, "Analysis of data separation and recovery problems using clustered sparsity", Proc. SPIE 8138, Wavelets and Sparsity XIV, 813818 (27 September 2011); doi: 10.1117/12.892723; https://doi.org/10.1117/12.892723
PROCEEDINGS
11 PAGES


SHARE
KEYWORDS
Data analysis

Wavelets

Algorithms

Associative arrays

Chemical elements

Phase modulation

Sensors

RELATED CONTENT

Application of wavelets in blind source separation
Proceedings of SPIE (November 13 2003)
Adaptation of document images to display constraints
Proceedings of SPIE (February 14 2008)
Local Fourier dictionary: a natural tool for data analysis
Proceedings of SPIE (October 26 1999)
Space-adaptive spectral analysis of hyperspectral imagery
Proceedings of SPIE (March 13 2003)

Back to Top