TY - GEN
T1 - Nonlinear basis pursuit
AU - Ohlsson, Henrik
AU - Yang, Allen Y.
AU - Dong, Roy
AU - Sastry, S. Shankar
PY - 2013
Y1 - 2013
N2 - In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In contrast to the existing nonlinear compressive sensing methods, the new algorithm is based on convex relaxation and is not a greedy method. The novel algorithm enables the compressive sensing approach to be used for a broader range of applications where there are nonlinear relationships between the measurements and the unknowns.
AB - In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In contrast to the existing nonlinear compressive sensing methods, the new algorithm is based on convex relaxation and is not a greedy method. The novel algorithm enables the compressive sensing approach to be used for a broader range of applications where there are nonlinear relationships between the measurements and the unknowns.
UR - http://www.scopus.com/inward/record.url?scp=84901285779&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84901285779&partnerID=8YFLogxK
U2 - 10.1109/ACSSC.2013.6810285
DO - 10.1109/ACSSC.2013.6810285
M3 - Conference contribution
AN - SCOPUS:84901285779
SN - 9781479923908
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 115
EP - 119
BT - Conference Record of the 47th Asilomar Conference on Signals, Systems and Computers
PB - IEEE Computer Society
T2 - 2013 47th Asilomar Conference on Signals, Systems and Computers
Y2 - 3 November 2013 through 6 November 2013
ER -