TwoDimensional Spectral Estimation: A Radon Transform Approach
projectsofme Active In SP Posts: 1,124 Joined: Jun 2010 
04102010, 02:32 PM
This article is presented by: K. R. RAMAKRISHNAN N. SRINIWASA ABSTRACT New technique for twodimensional (2D) 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 2D estimation problem is reduced to a set of onedimensional (1D) independent problems, which could then be solved using 1D linear prediction (LP) or by any other highresolution estimation procedure. This is unlike previous methods which obtain the 2D power spectral density (PSD) estimate by using 1D highresolution 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 INTRODUCTION In many applications of twodimensional (2D) 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 signaltonoise ratio (SNR) [l]. An extension to the 2D case is the use of onedimensional (1D) LP models along each of the dimensions. A class of 2D PSD estimators, known as the separable spectral estimators, employs 1D 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 highresolution 1D 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 1D AR models and bandlimited extrapolation.The techniques used, the 2D highresolution PSD was obtained by a separable operation, i.e., rowbyrow operation followed by columnbycolumn 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 2D sequence using 2D LP . However, in 2D 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 .. For more information about this article,please follow the link: googleurl?sa=t&source=web&cd=1&ved=0CBoQFjAA&url=http%3A%2F%2Feprints.iisc.ernet.in%2F3748%2F1%2Fradon.pdf&ei=hpapTPSiJoGavgPy7vz5DA&usg=AFQjCNHV3HQ0wE6M72wKq8GJiwABBfogww 



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