A Levinson-type algorithm for two-dimensional Wiener filtering using bivariate Szegö polynomials

Some Algorithms for the Recursive Input-Output Modeling of 2-D Systems.

“…The recursions that we obtain for ai(.,.) were first described in [20], [21], and they differ from those presented by Justice [22] by the fact that the orders n and m of a I in z and w can be increased separately (Justice's recursions were requiring that either n or m be fixed a priori). These recursions present also some similarity with the recursions derived by Genin and Kamp [23] for 2-D orthogonal polynomials on the unit hypercircle (see [17]- [18] and (24]- [27] for more details).…”

Stability of Methods for Solving Toeplitz Systems of Equations

“…Origin of Toeplitz systems. Toeplitz systems of linear equations arise from many sources [31], [54], [57]: (a) linear filtering [31], [39], [46], [61], (b) maximum entropy spectral analysis [59], (c) antennas and arrays [55], (d) estimates of shaping and matching filters [62], (e) recursive estimation [32]; image processing [1]; control theory: (a) minimal realization problem [14], [25], (b) minimal design problem [37], [38], (c) adaptive estimation of control system parameters [3]; statistics" (a) statistical communication and detection [50], (b) stationary auto-regressive time series [28]; integral equations [16], [48]: (a) convolution-type V01terra equations, (b) convolution-type Fredholm equations; orthogonal polynomials [27], [30], [34]; partial differential equations [42]" (a) elliptic, (b) parabolic; Pad6 approximation [6], [7], [8], [9], [24], [26].…”

A multidimensional Modelling approach to texture classification and segmentation

“…But up to now, in this general framework no particular generalisation of the Levinson algorithm has proven to prevail. The problem is, indeed, to interweave conveniently the recursions on p and r, and the current algorithms (5) reduce in fact to the case of a vector model identification as proposed here.…”

“…But, in fact, due to the stability problems (3) , (4) , generel non-separable bidimensional recursive fi1trs were not widely used in modelling. Furthermore, the attempts for introducing fast and efficient identification procedures (2d Levinson algorithm for instance) are fairly recent (5) , (6).…”