Two-dimensional orthogonal lattice structures for autoregressive modeling of random fields

Kayran, A.H.

doi:10.1109/78.492548

Cited by 33 publications

(10 citation statements)

References 23 publications

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“…Our initial motivation is to present a general 2-D lattice modeling technique which is capable of simultaneously providing all possible causal and noncausal models to obtain superior spectral estimation accuracy. Hence, this new formulation for constructing orthogonal backward prediction error vectors is quite different from the other attempts in [10], [12], and [17]. Table II shows the complexities of the existing 2-D lattice filters and proposed one.…”

Section: Remarks and Unification Of All Prediction Modelsmentioning

confidence: 95%

“…Determine and using (37). 2) Incrementing by unity, from , and reflection coefficient vectors, the horizontally augmented stage coefficient matrices, using (5), (10) and Table III are given as for and (38) Similarly, one can determine and by column and row reversal as in illustrated (37). 3) Incrementing by unity, vertically augmented stage coefficient matrices, using (16) and (17) are given as for and…”

Section: B 2-d Levinson Algorithm By Using Matricesmentioning

confidence: 99%

“…The results of this minimization are summarized in the following equation: (6) where (7) and (8) It is possible to derive a simple propagation equation for the auxiliary horizontal PEFs from th order to th order by recognizing that the expected value of the sum of the horizontal forward and backward prediction errors is , where is defined in (7), as follows. (9) The error propagation equations for the new initiated and existing auxiliary vertical forward/backward PEFs can be combined into a single structure, (10) where and are the reflection coefficient matrix and vectors, respectively, with , for . It is possible to write the th order vertical reflection coefficient matrix as .…”

Section: A Horizontal Recursive Order Incrementationmentioning

confidence: 99%

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New Efficient 2-D Lattice Structures for General Autoregressive Modeling of Random Fields

Kayran

Camcioglu

2014

IEEE Trans. Signal Process.

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In this paper, we present a new efficient general 2-D autoregressive (AR) lattice modeling technique of random fields. Our proposed approach is capable of simultaneously providing all possible types of 2-D causal quarter-plane (QP) and asymmetric half-plane (ASHP) AR models for an arbitrary rectangular shape of the prediction support region (PSR). It is shown that it is also possible to obtain various noncausal half-plane AR models without any additional computational cost. This new lattice structure introduces only one row or one column of new observation points into the existing rectangular PSR when the order of the model increases in the horizontal or vertical direction at each of the recursive order incrementation stage, respectively. Starting with a given random data field, a set of auxiliary forward and backward prediction error fields (PEFs) for the horizontal and vertical directions are generated. After recursive order updates to the desired size of the rectangular PSR, all types of causal QP/ASHP and noncausal half-plane 2-D lattice models are obtained by deriving the appropriate PEF from the remaining ones. In addition to developing the basic theory, the presentation includes the derivation of the synthesis model transfer functions from the calculated lattice parameters. It is shown that the proposed auxiliary horizontal and vertical backward prediction error filters inherently generates the mutually orthogonal realization vectors and thus are optimum for all stages. The theory has been confirmed by computer simulations.Index Terms-2-D signal processing, 2-D lattice filters, linear prediction, causal and noncausal modeling, 2-D spectral estimation.

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Section: Remarks and Unification Of All Prediction Modelsmentioning

confidence: 95%

Section: B 2-d Levinson Algorithm By Using Matricesmentioning

confidence: 99%

Section: A Horizontal Recursive Order Incrementationmentioning

confidence: 99%

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New Efficient 2-D Lattice Structures for General Autoregressive Modeling of Random Fields

Kayran

Camcioglu

2014

IEEE Trans. Signal Process.

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“…In this study, 2-D MYW equation is used to estimate the EAR coefficients of the ARMA process. The recently developed 2-D AR lattice algorithms [19,20] can be used for estimating the EAR parameters of the QP causal 2-D ARMA process with great accuracy. 2.…”

Section: Article In Pressmentioning

confidence: 99%

Estimation of 2-D ARMA model parameters by using equivalent AR approach

Kızılkaya

Kayran

2005

Journal of the Franklin Institute

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“…In this method, the solution of the Yule-Walker equations is computed faster. Some of the approaches have extended the 1-D lattice structures to 2-D AR models (Kayran 1996;Liu and Najim 1996;Marple and Lawrence 2000;Kayran and Camcioglu 2014).…”

mentioning

confidence: 99%

A new Levinson–Durbin based 2-D AR model parameter estimation method

Zeinali

Shafiee

2015

Multidim Syst Sign Process

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This paper presents a new method for estimating the parameters of quarterplane two dimensional (2-D) autoregressive model based on the Levinson-Durbin algorithm. To achieve this aim, one-dimensional formulations related to Levinson-Durbin algorithm are extended to 2-D case. Online parameter estimation, capability of parameters variation detection, estimation improvement by using new data and less computational requirement are the significant advantages of the proposed method. Because of not involving complex and time consuming matrix computations, the presented method is computationally efficient. Numerical simulations are presented to show the efficiency of the proposed approach.

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Two-dimensional orthogonal lattice structures for autoregressive modeling of random fields

Cited by 33 publications

References 23 publications

New Efficient 2-D Lattice Structures for General Autoregressive Modeling of Random Fields

New Efficient 2-D Lattice Structures for General Autoregressive Modeling of Random Fields

Estimation of 2-D ARMA model parameters by using equivalent AR approach

A new Levinson–Durbin based 2-D AR model parameter estimation method

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