Two-dimensional linear prediction models--part I: Spectral factorization and realization
- 1 February 1985
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Acoustics, Speech, and Signal Processing
- Vol. 33 (1), 280-299
- https://doi.org/10.1109/tassp.1985.1164523
Abstract
In this paper we present several results for three different canonical forms of linear prediction on a plane. These filters have causal, semicausal, and noncausal prediction geometries. Starting from their properties we consider the problem of realization of these filters from a given power spectral density function (SDF). Since it is not possible in general to obtain rational spectral factors of a two-dimensional SDF, we propose algorithms for obtaining rational approximations which are stable and converge to their limit (irrational) factors as the order of approximation is increased. It is also shown that the normal equations associated with the minimum variance two-dimensional prediction filters give a useful algorithm for obtaining rational approximations which are stable and converge to their unique limit filters. This result allows design of finite-order stable filters by solving a finite number of equations while realizing the given SDF arbitrarily closely.Keywords
This publication has 15 references indexed in Scilit:
- Advances in mathematical models for image processingProceedings of the IEEE, 1981
- Two-dimensional linear prediction: Autocorrelation arrays, minimum-phase prediction error filters, and reflection coefficient arraysIEEE Transactions on Acoustics, Speech, and Signal Processing, 1980
- Half-plane Toeplitz systemsIEEE Transactions on Information Theory, 1980
- A Fast Karhunen-Loeve Transform for Digital Restoration of Images Degraded by White and Colored NoiseIEEE Transactions on Computers, 1977
- A Fast Karhunen-Loeve Transform for a Class of Random ProcessesIEEE Transactions on Communications, 1976
- Two-dimensional spectral factorization with applications in recursive digital filteringIEEE Transactions on Acoustics, Speech, and Signal Processing, 1976
- Linear prediction: A tutorial reviewProceedings of the IEEE, 1975
- Two-dimensional discrete Markovian fieldsIEEE Transactions on Information Theory, 1972
- Prediction theory and Fourier Series in several variablesActa Mathematica, 1958
- On Stationary Processes in the PlaneBiometrika, 1954