Limited Projection 3D X-Ray Tomography Using the Maximum Entropy Method

Reconstruction of three-dimensional binary structures from an extremely limited number of cone-beam x-ray projections. Choice of prior

“…(i) The successive reduction in the number of required projections and views for the observation of the object [1][2][3][4][5][6], which is dictated by the limitations of accessibility of the object, x-ray dose and x-ray contrast. (ii) The improvement in the quality, the reduction of computing time and, by this, the spreading of the developed techniques to image restoration of objects with arbitrary boundaries and contrast [4,[7][8][9][10][11][12][13][14].…”

“…The a priori knowledge gives a way to moderately reduce the demand for input data. Usually the a priori information is introduced in form of functionals [3,[7][8][9][12][13][14] that tend to support, in weighted form, some important expected features of the reconstructed image, such as smoothness [15,16], minimal summarized grey level in the image [7], monotonicity, convexity, porosity [17], etc. Much power is enclosed in the statistical methods for reconstruction [18][19][20] that support the maximum entropy, minimal Gibbs energy or other probabilistic priors in the image under restoration.…”

“…In [12][13][14] it was shown that the step of reducing the space of interest before starting the iteration procedure opens up one way to a wide range of applications for variational methods in reconstruction from limited projections. This is provided by some formal algorithms, based on the compatibility of the 2D images given by the projections.…”

“…In [12][13][14] a technique is proposed for the further improvement of the reconstruction capabilities for arbitrary binary structures using an extremely small number of projections, a limited number of views for the observation, and a priori knowledge introduced in a very general form. The present article summarizes and generalizes this approach for the restoration of 3D binary images of arbitrary objects from 2D projection data from non-predefined x-ray source locations and favouring flatness and/or volumetricity of the structure under restoration.…”