Title :
Multidimensional signal reconstruction from multichannel acquisition
Author :
Law, Ka Lung ; Fossum, Robert M. ; Do, Minh N.
Author_Institution :
Dept. of Math., Univ. of Illinois at Urbana-Champaign, Urbana-Champaign, IL
Abstract :
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.
Keywords :
FIR filters; matrix algebra; signal reconstruction; FIR analysis filters; FIR synthesis polyphase matrices; matrix invertibility; maximum sampling rate; multichannel acquisition; multidimensional signal reconstruction; sampling matrices; synthesis matrix; Algorithm design and analysis; Convolution; Filter bank; Finite impulse response filter; Matrix decomposition; Multidimensional systems; Sampling methods; Signal analysis; Signal reconstruction; Signal synthesis; Hermite Normal Form; Inverse Matrix Problem; Multichannel convolution; Perfect Reconstruction; Smith Normal Form;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on
Conference_Location :
Taipei
Print_ISBN :
978-1-4244-2353-8
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2009.4960305
