COMPARATIVE-STUDY OF THE USE OF LINEAR AND MODIFIED CUBIC SPLINE INTERPOLATION FOR IMAGE-RECONSTRUCTION

Image reconstruction is the process of recovering a function of two variables from experimentally obtained estimates of its integrals alone certain lines. An important version in medicine is the recovery of the density distribution within a cross-section of the human body from a number of X-ray projections. A computationally efficient technique for image reconstruction is the so-called convolution method. It consists of two steps: (i) data obtained by each of the orojections of the cross-section are separately (discrete) convolved with a fixed function; (ii) the density of the function at any point in the cross-section is estimated as the sum of values (one from each projection) of the convolved projection data. A difficulty is that part (ii) usually requires values of the convolved projection data at points other than where they have been calculated during part (i). This is usually resolved by interpolation between the calculated values. In this paper we report on a computer experimental study which compares the efficacy of two methods of interpolation (linear interoolation and a modified cubic spline interpolation) when used with the convolution reconstruction method. The two interoolation techniques are examined for their mathematical properties and are compared from the points of view of resolution of fine details, smoothness of the reconstructed cross-sections, sensitivity to noise in the data, the overall nearness of the original and reconstructed objects, and the cost of implementation. Both methods are illustrated on reconstructions of a mathematically described cross-section of the human head from computer simulated X-ray data. © 1979 IEEE.