TY - GEN

T1 - Sparse regularized total least squares for sensing applications

AU - Zhu, Hao

AU - Leus, Geert

AU - Giannakis, Georgios B.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - This paper focuses on solving sparse reconstruction problems where we have noise in both the observations and the dictionary. Such problems appear for instance in compressive sampling applications where the compression matrix is not exactly known due to hardware non-idealities. But it also has merits in sensing applications, where the atoms of the dictionary are used to describe a continuous field (frequency, space, angle, ... ). Since there are only a finite number of atoms, they can only approximately represent the field, unless we allow the atoms to move, which can be done by modeling them as noisy. In most works on sparse reconstruction, only the observations are considered noisy, leading to problems of the least squares (LS) type with some kind of sparse regularization. In this paper, we also assume a noisy dictionary and we try to combat both noise terms by casting the problem into a sparse regularized total least squares (SRTLS) framework. To solve it, we derive an alternating descent algorithm that converges to a stationary point at least. Our algorithm is tested on some illustrative sensing problems.

AB - This paper focuses on solving sparse reconstruction problems where we have noise in both the observations and the dictionary. Such problems appear for instance in compressive sampling applications where the compression matrix is not exactly known due to hardware non-idealities. But it also has merits in sensing applications, where the atoms of the dictionary are used to describe a continuous field (frequency, space, angle, ... ). Since there are only a finite number of atoms, they can only approximately represent the field, unless we allow the atoms to move, which can be done by modeling them as noisy. In most works on sparse reconstruction, only the observations are considered noisy, leading to problems of the least squares (LS) type with some kind of sparse regularization. In this paper, we also assume a noisy dictionary and we try to combat both noise terms by casting the problem into a sparse regularized total least squares (SRTLS) framework. To solve it, we derive an alternating descent algorithm that converges to a stationary point at least. Our algorithm is tested on some illustrative sensing problems.

KW - Direction-of-arrival estimation

KW - Sparsity

KW - Spectrum sensing

KW - Total least squares (TLS)

UR - http://www.scopus.com/inward/record.url?scp=78751487418&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78751487418&partnerID=8YFLogxK

U2 - 10.1109/SPAWC.2010.5671061

DO - 10.1109/SPAWC.2010.5671061

M3 - Conference contribution

AN - SCOPUS:78751487418

SN - 9781424469901

T3 - IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC

BT - 2010 IEEE 11th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2010

T2 - 2010 IEEE 11th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2010

Y2 - 20 June 2010 through 23 June 2010

ER -