Toeplitz properties of the block matrices encountered in the processing of spatiotemporal signals

Various signal processing applications, such as system identification, FIR (finite impulse response) Wiener filtering, linear prediction, and spectral estimation, are known to lead to the solution of Toeplitz systems for the case of one-dimensional signals and to Toeplitz-block Toeplitz systems for the case of two-dimensional signals. The authors investigate such systems for the case of L-dimensional signals with L>2 and emphasize their block and persymmetrical nature. Such important characteristics allow the use of fast algorithms for signals of any dimension. The case of three-dimensional signals is treated in detail not only because it is of special interest for video applications, but also because the reasoning used for this case can be straightforwardly applied to higher-dimension signals