Abstract

New signal/image processing algorithms involving the Radon transform are presented. Algorithms that address computed tomography (CT) are motivated by the desire to process within the Radon space, instead of post-processing a reconstructed image. Algorithms that use the Radon transform as a tool, exploit the properties of the transform to simplify a 2-D processing task. New image-invariants based on the moments of the projections are developed. The notion of moment-patterns in the Radon space is introduced. A method of rendering the moment-patterns invariant to geometric transformations is presented. An alternative descriptor based on the moment-patterns, invariant to geometric transformations as well as contrast, is proposed. Selective reconstruction of objects from noisy projections is considered as an application of the 'instantaneous matched-filter'. It involves a combination of the ideas of detection of an object of known shape and location, and an estimation of the associated parameter. A new approach to binary image compression is proposed, based on a representation of binary objects by a small number of projections. Additional compression is obtained by coding the 1-D non-binary projections. The approach finds applications (i) in CT, involving binary densities, and (ii) as a method of compressing binary images. A new algorithm developed for reconstructing binary images from their projections, turns out to be a variant of the algebraic reconstruction technique. Two-dimensional spectral factorization in the Radon space is discussed, and some new applications are indicated. The theory suggests a new approach to 2-D spectrum estimation using the Radon transform, which is considered in the sequel. Some of the issues associated with the Radon transform of a stationary random field are brought out. A new representation for the Radon transform of a stationary random field (valid upto second-order statistics), is used to study the second-order properties of the transform. Limitations pertaining to the theory and its application to random field data over a finite support, are discussed. A novel approach to spectrum estimation based on the Radon transform of 2-D autocorrelation of the stationary random field data is investigated. Estimation by autoregressive modeling is considered, and an extension to the maximum entropy method is discussed