Marina Chukalina

Anastasiya Dolmatova, Marina Chukalina, Dmitry Nikolaev

Filtered back projection (FBP) is a commonly used technique in tomographic image reconstruction demonstrating acceptable quality. The classical direct implementations of this algorithm require the execution of $Θ(N^3)$ operations, where $N$ is the linear size of the 2D slice. Recent approaches including reconstruction via the Fourier slice theorem require $Θ(N^2\log N)$ multiplication operations. In this paper, we propose a novel approach that reduces the computational complexity of the algorithm to $Θ(N^2\log N)$ addition operations avoiding Fourier space. For speeding up the convolution, ramp filter is approximated by a pair of causal and anticausal recursive filters, also known as Infinite Impulse Response filters. The back projection is performed with the fast discrete Hough transform. Experimental results on simulated data demonstrate the efficiency of the proposed approach.

V. Kokhan, M. Grigoriev, A. Buzmakov et al.

Porous materials are widely used in different applications, in particular they are used to create various filters. Their quality depends on parameters that characterize the internal structure such as porosity, permeability and so on. Computed tomography (CT) allows one to see the internal structure of a porous object without destroying it. The result of tomography is a gray image. To evaluate the desired parameters, the image should be segmented. Traditional intensity threshold approaches did not reliably produce correct results due to limitations with CT images quality. Errors in the evaluation of characteristics of porous materials based on segmented images can lead to the incorrect estimation of their quality and consequently to the impossibility of exploitation, financial losses and even to accidents. It is difficult to perform correctly segmentation due to the strong difference in voxel intensities of the reconstructed object and the presence of noise. Image filtering as a preprocessing procedure is used to improve the quality of segmentation. Nevertheless, there is a problem of choosing an optimal filter. In this work, a method for selecting an optimal filter based on attributive indicator of porous objects (should be free from 'levitating stones' inside of pores) is proposed. In this paper, we use real data where beam hardening artifacts are removed, which allows us to focus on the noise reduction process