A two-dimensional fast lattice recursive least squares algorithm

This paper is mainly devoted to the derivation of a new two-dimensional fast lattice recursive least squares (2D FLRLS) algorithm. This algorithm updates the filter coefficients in growing-order form with linear computational complexity. After appropriately defining the "order" of 2D data and exploiting the relation with 1D multichannel, "order" recursion relations and shift invariance property are derived. The geometrical approaches of the vector space and the orthogonal projection then can be used for solving this 2D prediction problem. We examine the performances of this new algorithm in comparison with other fast algorithms.

[1]  Thomas Kailath,et al.  Least-squares adaptive lattice and transversal filters: A unified geometric theory , 1984, IEEE Trans. Inf. Theory.

[2]  Stefanos D. Kollias,et al.  A fast multichannel approach to adaptive image estimation , 1989, IEEE Trans. Acoust. Speech Signal Process..

[3]  B. Porat,et al.  Digital Spectral Analysis with Applications. , 1988 .

[4]  A. H. Kayran,et al.  Lattice parameter autoregressive modeling of two-dimensional fields--Part I: The quarter-plane case , 1984 .

[5]  George-Othon Glentis,et al.  Fast adaptive algorithms for multichannel filtering and system identification , 1992, IEEE Trans. Signal Process..

[6]  T. Kailath,et al.  Numerically stable fast transversal filters for recursive least squares adaptive filtering , 1991, IEEE Trans. Signal Process..

[7]  C. W. Therrien,et al.  A new 2-D fast RLS algorithm , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[8]  S. Parker,et al.  Lattice-filter modeling of two-dimensional fields , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  F. Ling,et al.  A generalized multichannel least squares lattice algorithm based on sequential processing stages , 1984 .

[10]  T. Kailath,et al.  Fast, recursive-least-squares transversal filters for adaptive filtering , 1984 .

[11]  Mohamed Najim,et al.  Implementation of the stabilized fast transversal filter algorithm on fixed point DSP , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  Hanoch Lev-Ari,et al.  Modular architectures for adaptive multichannel lattice algorithms , 1983, IEEE Trans. Acoust. Speech Signal Process..

[13]  M. Morf,et al.  Square root covariance ladder algorithms , 1982 .

[14]  Hideaki Sakai,et al.  Recursive least squares circular lattice and escalator estimation algorithms , 1983 .

[15]  George-Othon Glentis,et al.  Fast algorithms for 2-D least squares FIR filtering , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[16]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[17]  C. Therrien.  Relations between 2-D and multichannel linear prediction , 1981 .

[18]  John M. Cioffi,et al.  Limited-precision effects in adaptive filtering , 1987 .

[19]  T. Marzetta.  Two-dimensional linear prediction: Autocorrelation arrays, minimum-phase prediction error filters, and reflection coefficient arrays , 1980 .

[20]  Mohamed Najim,et al.  Two-dimensional joint process lattice for adaptive restoration of images , 1992, IEEE Trans. Image Process..

[21]  Bishwa Nath Mukherjee,et al.  The foundations of multivariate analysis : a unified approach by means of projection onto linear subspaces , 1984 .

[22]  Lennart Ljung,et al.  Error propagation properties of recursive least-squares adaptation algorithms , 1985, Autom..

[23]  S. R. Parker,et al.  Orthogonal Two-Dimensional Lattice Filters , 1985, Nineteeth Asilomar Conference on Circuits, Systems and Computers, 1985..

[24]  Paul S. Lewis,et al.  QR-based algorithms for multichannel adaptive least squares lattice filters , 1990, IEEE Trans. Acoust. Speech Signal Process..

[25]  Martin Morf,et al.  Ladder Forms Lin Estimation And System Identification , 1977 .

[26]  M. Morf,et al.  Recursive least squares ladder estimation algorithms , 1981 .

[27]  Aysin Ertüzün,et al.  An improved 2-D lattice filter and its entropy relations , 1992, Signal Process..

[28]  Dan E. Dudgeon,et al.  Multidimensional Digital Signal Processing , 1983 .

[29]  B. Friedlander,et al.  Lattice filters for adaptive processing , 1982, Proceedings of the IEEE.

[30]  George Carayannis,et al.  A fast sequential algorithm for least-squares filtering and prediction , 1983 .