TY - GEN
T1 - Generalized Vandermonde decomposition and its use for multi-dimensional super-resolution
AU - Yang, Zai
AU - Xie, Lihua
AU - Stoica, Petre
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/9/28
Y1 - 2015/9/28
N2 - The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multi-dimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided under appropriate conditions. The new result is also used to study MD frequency estimation from compressive data within the recent super-resolution framework. A systematic approach is proposed and a numerical simulation is provided to demonstrate its effectiveness compared to the existing atomic norm method.
AB - The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multi-dimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided under appropriate conditions. The new result is also used to study MD frequency estimation from compressive data within the recent super-resolution framework. A systematic approach is proposed and a numerical simulation is provided to demonstrate its effectiveness compared to the existing atomic norm method.
KW - The Vandermonde decomposition
KW - atomic norm
KW - multi-dimensional frequency estimation
KW - multilevel Toeplitz matrix
KW - super-resolution
UR - https://www.scopus.com/pages/publications/84969753178
U2 - 10.1109/ISIT.2015.7282808
DO - 10.1109/ISIT.2015.7282808
M3 - 会议稿件
AN - SCOPUS:84969753178
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2011
EP - 2015
BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - IEEE International Symposium on Information Theory, ISIT 2015
Y2 - 14 June 2015 through 19 June 2015
ER -