Multidimensional signal reconstruction from multichannel acquisition

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.