On Two-Dimensional Maximum Entropy Spectral Estimation

A novel method of two-dimensional (2-D) spectral estimation, which we introduced recently using the Radon transform and a one dimensional (1-D) autoregressive model, led us to investigate the maximization of entropy subject to the correlation matching constraints in the Radon space. Instead of solving the 2-D maximum entropy spectral estimation problem, we convert it into a problem which is easier to solve. It is shown that a radial slice of the 2-D ME spectrum can be obtained by 1-D AR modeling of the projections (Radon transform) of a stationary random field (SRF). The advantages and limitations of using this new duality relation to estimate the complete 2-D ME spectra on a polar raster are discussed

Two-Dimensional Spectral Estimation: A Radon Transform Approach

A 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 [19]. Using the Radon transform, the 2-D estimation problem is reduced to a set of one-dimensional (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 [2]. Examples are provided to illustrate the performance of the new technique. Various features of this approach are highlighted

Detection of edges from projections

In a number of applications of computerized tomography, the ultimate goal is to detect and characterize objects within a cross section. Detection of edges of different contrast regions yields the required information. The problem of detecting edges from projection data is addressed. It is shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data. This not only reduces the computational burden but also avoids the difficulties of postprocessing a reconstructed image. This is accomplished by a convolution backprojection operation. For example, with the Marr-Hildreth edge detection operator, the filtering function that is to be used on the projection data is the Radon transform of the Laplacian of the 2-D Gaussian function which is combined with the reconstruction filter. Simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presente

Detecting Edges From Projections

In a number of applications of computerized tomography, the ultimate goal is to detect and characterize objects within a cross section. Detection of edges of different contrast regions yields the required information. This paper addresses the problem of detecting edges from projection data. It has been shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data. This not only reduces the computational burden but also avoids getting into difficulties of postprocessing a reconstructed image. This is accomplished by a convolution backprojection operation. For example, with the Marr-Hildreth edge detection operator, the filtering function that is to be used on the projection data is the Radon transform of the Laplacian of the 2-D Gaussian function which is combined with the reconstruction filter. Simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presented

On a programmable signal processor for VLSI

This paper presents a method of designing a programmable signal processor based on a bit parallel matrix vector matrix multiplier (linear transformer). The salient feature of this design is that the efficiency of the direct vector matrix multiplier is improved and VLSI design is made much simpler by trading off the more expensive arithematic operation (multiplication) for 'cheaper' manipulation (addition/subtraction) of the data

On Two-Dimensional Maximum Entropy Spectral Estimation

A novel method of two-dimensional (2-D) spectral estimation, which we introduced recently using the Radon transform and a one dimensional (1-D) autoregressive model, led us to investigate the maximization of entropy subject to the correlation matching constraints in the Radon space. Instead of solving the 2-D maximum entropy spectral estimation problem, we convert it into a problem which is easier to solve. It is shown that a radial slice of the 2-D ME spectrum can be obtained by 1-D AR modeling of the projections (Radon transform) of a stationary random field (SRF). The advantages and limitations of using this new duality relation to estimate the complete 2-D ME spectra on a polar raster are discussed

Image Reconstruction Form Truncated Projections : A Linear Predication Approach

Unambiguous reconstruction is not possible with truncated projections. In order to reduce the ambiguity in the reconstructed image, several authors have suggested that a simple 'completion' involving extrapolation of the truncated projection is sufficient. In this paper a method based on a Linear Prediction approach is proposed for obtaining the missing part in the projection. Reconstruction is then carried out using the Convolution Backprojection (CBP) method [1]. Simulation results showing the effectiveness of this method in extracting significantly more information from truncated projections are presented