International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: 05 80 116905-7474 IJET-IJENS @ October 2011 IJENS I J E N S Tomographic Image Reconstruction from a Sparse Projection Data Using Sinogram Interpolation Catur Edi Widodo, Kus Kusminarto, Gede Bayu Suparta Abstract - In this paper we propose a new approach of tomographic image reconstruction using sinogram interpolation for a sparse projection data. In this term, sinogram interpolation is a process of converting a sampled projection to a higher sampling rate projection. By using interpolation, we construct a new projections within the range of set of projection, then we apply a filtered backprojection reconstruction to get the tomographic image. This proposed approach reconstruction is applied to simulated half full angle projection data of the Shepp-Logan phantom with sparse angular sampling. The result are better than those given by filtered backprojection reconstruction without sinogram interpolation. Keyword - tomography, projection, sinogram, interpolation, backprojection I. INTRODUCTION In tomography, the inner structure of object is reconstructed from a collection of projection data. The widely used computerized tomography (CT) imaging uses an extensive set of projections acquired from all around the body. Reconstruction from such complete data is by now well understood, most popular method being filtered back- projection [1]. In medical tomography, it is important to consider the dose received by patient because the greater the radiation dose, the greater the risk of tissue damage and the risk of cancer [2], [3]. Many strategies have been proposed to reduce dose by minimizing radiation exposure but using low dose may result quantum noise [2]. This quantum noise can be reduced by appliying suitable filter on sinogram from scanning object. Bharkada et. al. [4] reduce dose radiation by appliying normal dose for region of interest (ROI) object and appliying very low dose for non ROI object. The widely used method to reduce dose is by reducing the number of projections by widening the projection angel interval. We refer to this types of incomplete data as sparse projection data. The weakness of this method is in the image reconstruction results will arise an artefact defect. By using the evolution theory [1], wavelet transform [3], convex projection method [5], total variation [6], and metric labeling [7], reconstruction can be done without causing artefact defect using ten projections only. All works we have described above are iterative methods. This method is based on idea of solving a system of linear equations in which the linear attenuation coefficient distribution of the object, μ(x,y), and its projection, p ø (x r ), are considered as discrete matrices, M and P, respectively. These two matrices are related by P = RM, when R is a matrix transformation that describes the Radon transform operation. The objective is then to find the inverse transform operator, R -1 [8]. All iterative methods commence from initial guess for M 0 . From this the projections, P, are determined and compared to experimental values of P exp . The projection errors is then used to form a corrected projection set which is subsequently used to produce the new value of M 1 . In the algebraic reconstruction technique (ART), the projection error used to correct projection is exactly ΔP = P exp – P, but in further technique (partly we describe above is convex projection, evolution theory, and total variation) is determined by statistical consideration. The aim of our work is to propose a new approach, where we do interpolate the sinogram with sparse projection then perform backprojection to get the reconstructed image. II. ALGORITHM The Radon Transform has several useful properties [9] (Table 1). The property of linearity can be described as follow: Suppose there are N objects, each of object has the functions of f 1 (x,y), f 2 (x,y), ..., f n (x,y), and each function is multiplied by the scalar a 1 , a 2 , ..., a n , the Radon transform of linear combination all of these functions is same as linear combination of each of its Radon transform. The projections g(s, ө) are space limited in s if the object f(x,y) is space limited in (x,y), and they are periodic in ө with period 2π. A translation of f(x,y) results in the shift of g(s,ө) by a distance equal to the projection of the translation vector on the line s = x cos ө + y sin ө. A rotation of the object by an angle ө causes a translation of its Radon transform in the variable ө. A scaling of the (x,y) coordinates of f(x,y) results in scaling of the s coordinate together with an amplitude scaling of g(s,ө). Finally, the total mass of distribution f(x,y) is preserved by g(s,ө) for all ө.