# X-Ray Coded Source Tomosynthesis

## Abstract

We consider the problem of reconstructing a 3-D object from its 2-D coded radiograph. A new approach to the solution of the problem is presented. The proposed method consists of computing a set of optimal decoding functions using the Kaczmarz algebraic iterative algorithm. To this end, an approximately space-invariant ‘3-D standard response’ is introduced which can be used to characterize any coded source imaging system. Each decoding function corresponds to a specific depth plane inside the object to be reconstructed. The result is a set of 2-D tomograms, each of which is obtained by correlating the coded radiograph with the corresponding decoding function. Two ways of computing the decoding functions are discussed: (i) considering only a single object slice; (ii) treating several immediately adjacent slices (possibly all of them) simultaneously. The proposed reconstruction method can be used for any planar arrangement of discrete sources and is thus capable of comparing the performance of various source point distributions. It is shown that a nine redundant source code provides for better reconstructions than a twelve circular array and a twelve nonredundant array (of same inertia). Finally, the reconstruction of a simulated five planes object using the nine redundant array code is presented.

## Keywords

Point Spread Function Circular Array Depth Plane Continuous Object Decode Function## Preview

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