Spatial Resolution Analysis for Few-Views Discrete Tomography Based on MART-AP Algorithm

We study a new MART-AP algorithm of few-views discrete tomography. Its efficiency for high-frequency structure reproduction is investigated in a numerical experiment where we reconstruct a 2D model for the estimation of the spatial resolution limit. We estimate the modulation transfer function of the reconstruction algorithm and compare it with the modulation transfer function of projection distortions. Our results show that MART-AP weakly influences the contrast of spatial structures being reproduced and can be used for high-resolution reconstruction when only a few projections are registered. 1. Introduction We have recently seen a growing interest to few-views computed tomography [1]. A need to reconstruct the inner structure of an object in conditions when a few projections (usually less than 10) are only registered arises in many areas of tomography applications. These are, for example, nondestructive testing in industry [2, 3], luggage inspection [3, 4], plasma emission tomography [5], tomography of explosion-compressed metal shells [6], fast detonation research [7], and other. The main problem of few-views tomography is that reconstructed images are not free from artifacts which result from strongly limited data and make the reproduction of spatial structures less accurate. It is not easy to compensate the artifacts and as a rule, the problem is resolved through the use of a priori information about the object [8]. In doing so, the leading role is given to methods of discrete tomography [9–11], which use a priori information on the discrete values of the object function to be reconstructed. What is of great importance is the way in which this information is incorporated into the image. Until recently, the Bayesian reconstruction techniques [8–12] were thought to be most effective in terms of the ease of a priori information incorporation. Now more often different modifications to the well-known algebraic reconstruction technique [1] are applied to solve this problem. As an example, we can refer to an algorithm [13] based on a multistep procedure where each iteration includes segmentation with a priori information and then correction of intensities in cells which are near the boundaries of the contrast structures. In our recent work [14], we proposed a discrete tomography algorithm based on the multiplicative algebraic reconstruction technique (MART). We call it MART-AP (an MART which uses a priori information). Our algorithm, like that one described in [13], is based on a multistep solution correction procedure. But we apply corrections