TY - GEN
T1 - Beyond Moore-Penrose
T2 - 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
AU - Dokmanic, Ivan
AU - Kolundzija, Mihailo
AU - Vetterli, Martin
PY - 2013/10/18
Y1 - 2013/10/18
N2 - Frequently, we use the Moore-Penrose pseudoinverse (MPP) even in cases when we do not require all of its defining properties. But if the running time and the storage size are critical, we can do better. By discarding some constraints needed for the MPP, we gain freedom to optimize other aspects of the new pseudoinverse. A sparser pseudoinverse reduces the amount of computation and storage. We propose a method to compute a sparse pseudoinverse and show that it offers sizable improvements in speed and storage, with a small loss in the least-squares performance. Differently from previous approaches, we do not attempt to approximate the MPP, but rather to produce an exact but sparse pseudoinverse. In the underdetermined (compressed sensing) scenario we prove that the rescaled sparse pseudoinverse yields an unbiased estimate of the unknown vector, and we demonstrate its potential in iterative sparse recovery algorithms, pointing out directions for future research.
AB - Frequently, we use the Moore-Penrose pseudoinverse (MPP) even in cases when we do not require all of its defining properties. But if the running time and the storage size are critical, we can do better. By discarding some constraints needed for the MPP, we gain freedom to optimize other aspects of the new pseudoinverse. A sparser pseudoinverse reduces the amount of computation and storage. We propose a method to compute a sparse pseudoinverse and show that it offers sizable improvements in speed and storage, with a small loss in the least-squares performance. Differently from previous approaches, we do not attempt to approximate the MPP, but rather to produce an exact but sparse pseudoinverse. In the underdetermined (compressed sensing) scenario we prove that the rescaled sparse pseudoinverse yields an unbiased estimate of the unknown vector, and we demonstrate its potential in iterative sparse recovery algorithms, pointing out directions for future research.
KW - Efficient computation
KW - Moore-Penrose pseudoinverse
KW - sparse pseudoinverse
UR - http://www.scopus.com/inward/record.url?scp=84890492397&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84890492397&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2013.6638923
DO - 10.1109/ICASSP.2013.6638923
M3 - Conference contribution
AN - SCOPUS:84890492397
SN - 9781479903566
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 6526
EP - 6530
BT - 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Y2 - 26 May 2013 through 31 May 2013
ER -