Deterministic Defuzzification Based on Spectral Projected Gradient Optimization

Limited-view binary tomography reconstruction assisted by shape centroid

“…Bone image is obtained from a histological CT image of a bone implant, inserted in a leg of a rabbit [36]. Cell is a binary segmented fluorescence image of a calcein-stained Chinese hamster ovary cell [24,39]. The results obtained by the proposed method, in the following denoted by CENT, based on the centroid prior are compared to other methods relevant for the case of low projection availability.…”

Deterministic discrete tomography reconstruction by energy minimization method on the triangular grid

“…We note that similar reconstruction approaches, including the SPG algorithm, had also been successfully used within the reconstruction process on classical/rectangular gird, see [18,20].…”

Regularized binary tomography on the hexagonal grid

“…Therefore, our goal is to propose a new energy minimization type reconstruction method for hexagonal grid based on an appropriate deterministic optimization method. The choice is the Spectral Projected Gradient (SPG) algorithm [32], already suggested for similar problems on the square grid [33][34][35]. The used regularization is also changed and instead of the Gibbs prior we apply a smoothing term considering neighbor hexels around each grid hexel.…”

“…Similar reconstruction approaches, including the SPG algorithm, have also been successfully used within the reconstruction process on classical (square) grid, see [33,34] and on the triangular grid [27,29]. In this paper, the third regular grid, the hexagonal grid is addressed and the algorithm is adapted.…”