TY - GEN
T1 - Multidimensional signal reconstruction from multichannel acquisition
AU - Ka, Lung Law
AU - Fossum, Robert M.
AU - Do, Minh N.
N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - We provide an analysis of the algorithms necessary for the optimal use of multidimensional signal reconstruction from multichannel acquisition. First, we provide computable conditions to test the matrix invertibility and propose algorithms to find a particular inverse. Second, we determine the existence of perfect reconstruction systems for given FIR analysis filters with some sampling matrices and some FIR synthesis polyphase matrices. Then, we present the development of an efficient algorithm designed to find a sampling matrix with maximum sampling rate and FIR synthesis polyphase matrix for given FIR analysis filters so that the system provides a perfect reconstruction. Once a particular synthesis matrix is found, we can characterize all synthesis matrices and find an optimal one according to a design criterion.
AB - We provide an analysis of the algorithms necessary for the optimal use of multidimensional signal reconstruction from multichannel acquisition. First, we provide computable conditions to test the matrix invertibility and propose algorithms to find a particular inverse. Second, we determine the existence of perfect reconstruction systems for given FIR analysis filters with some sampling matrices and some FIR synthesis polyphase matrices. Then, we present the development of an efficient algorithm designed to find a sampling matrix with maximum sampling rate and FIR synthesis polyphase matrix for given FIR analysis filters so that the system provides a perfect reconstruction. Once a particular synthesis matrix is found, we can characterize all synthesis matrices and find an optimal one according to a design criterion.
KW - Hermite normal form
KW - Inverse matrix problem
KW - Multichannel convolution
KW - Perfect reconstruction
KW - Smith normal form
UR - http://www.scopus.com/inward/record.url?scp=70349205448&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70349205448&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2009.4960305
DO - 10.1109/ICASSP.2009.4960305
M3 - Conference contribution
AN - SCOPUS:70349205448
SN - 9781424423545
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3201
EP - 3204
BT - 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009
T2 - 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009
Y2 - 19 April 2009 through 24 April 2009
ER -