Two-Dimensional Spectral Estimation: A Radon Transform Approach
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04-10-2010, 02:32 PM

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New technique for two-dimensional (2-D) spectral estimation of a stationary random field (SRF) is investigated in this paper. This is based on the extension of the Radon transform theory to stationary random fields (SRF’s), proposed by Jain and Ansari . Using the Radon transform, the 2-D estimation problem is reduced to a set of onedimensional (1-D) independent problems, which could then be solved using 1-D linear prediction (LP) or by any other high-resolution estimation procedure. This is unlike previous methods which obtain the 2-D power spectral density (PSD) estimate by using 1-D high-resolution techniques in the spirit of a separable estimator . Examples are provided to illustrate the performance of the new technique. Various features of this approach are highlighted

In many applications of two-dimensional (2-D) signal processing such as sonar, radar, geophysics, and radio astronomy, the problem of estimation of the power spectral density (PSD) of a sampled stationary random field (SRF) from a finite set of observations is often encountered. The classical method of estimation of PSD using the periodogram results in poor resolution. A recent approach to obtain a highresolution estimate is to postulate a finte parametric model for the PSD. The observations are used to obtain the model parameters by an appropriate estimate procedure. In one dimension, the modeling techniques employing linear prediction (LP) theory have been widely investigated anda re successfully being used to obtain the PSD estimate especially at a high signal-to-noise ratio (SNR) [l]. An extension to the 2-D case is the use of one-dimensional (1-D) LP models along each of the dimensions. A class of 2-D PSD estimators, known as the separable spectral estimators, employs 1-D estimation techniques sequentially along each of the dimensions . Since it is crucial that the phase not be discarded at the intermediate discrete Fourier transform (DFT) is used along the first dimension and a high-resolution 1-D autoregressive (AR) spectral estimator along the other dimension. The resolution obtained along the first dimension is restricted by the DFT. Higher resolution along the first dimension is obtained by artificially extending the data while preserving the phase as well. The techniques used for generating additional data include the use of 1-D AR models and band-limited extrapolation.The techniques used, the 2-D high-resolution PSD was obtained by a separable operation, i.e., row-by-row operation followed by column-by-column operation. In the presence of noise, as is the case in all applications, this separable class of estimation is not justified . Further, separable estimation ignores the correlation between rows and columns. The interdimensional correlation is exploited by modeling the 2-D sequence using 2-D LP . However, in 2-D modeling, the choice of the model and the associated predictor filter mask, the appropriate order for the model, the order of computation of the model parameters, and the resulting characteristics of the spectral estimate are the major issues ..

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