A MajorizeMinimize memory gradient algorithm applied to Xray tomography Some recent efforts on image restoration have been extended to tomographic reconstruction methods with apriori information so that situations with higher amounts of noise or lesser amounts of projections could be better dealt with. This paper deals with the reconstruction of a two or threedimensional image from a small set of tomographic projections (i.e. a small number of projection angles). We adopt a variational reconstruction approach, with smooth regularization on the image gradient for reconstruction. The MajorizeMinimize Memory Gradient algorithm is our proposed solution for the optimization problem. The performance of the proposed strategy is illustrated through synthetic and real image reconstruction examples. The reconstruction error is investigated for convex and nonconvex penalization strategies, as a function of the number of tomographic measurements and the noise level. The nonconvex approach turns out to be more efficient in the case of binary images. In contrast, convex penalization seems to give better results for multilabel or natural images.

Sparse filtered SIRT for electron tomography Abstract   Electron tomographic reconstruction is a method for obtaining a threedimensional image of a specimen with a series of two dimensional microscope images taken from different viewing angles. Filtered backprojection, one of the most popular tomographic reconstruction methods, does not work well under the existence of image noises and missing wedges. This paper presents a new approach to largely mitigate the effect of noises and missing wedges. We propose a novel filtered backprojection that optimizes the filter of the backprojection operator in terms of a reconstruction error. This datadependent filter adaptively chooses the spectral domains of signals and noises, suppressing the noise frequency bands, so it is very effective in denoising. We also propose the new filtered backprojection embedded within the simultaneous iterative reconstruction iteration for mitigating the effect of missing wedges. Our numerical study is presented to show the performance gain of the proposed approach over the stateoftheart.