A Convex Formulation for Binary Tomography

@article{Kadu2020ACF,
  title={A Convex Formulation for Binary Tomography},
  author={Ajinkya Kadu and Tristan van Leeuwen},
  journal={IEEE Transactions on Computational Imaging},
  year={2020},
  volume={6},
  pages={1-11}
}
Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a constrained least-squares problem. As the constraints are nonconvex, many approaches for solving it rely on either relaxing the constraints or heuristics. In this paper, we propose a novel convex formulation, based on the Lagrange dual of the constrained least-squares… Expand
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References

SHOWING 1-10 OF 50 REFERENCES
Binary Tomography Using Gibbs Priors
TLDR
The time-consuming nature of the stochastic reconstruction algorithm is ameliorated by a preprocessing step that discovers image locations at which the value is the same in all images having the given projections; this reduces the search space considerably. Expand
An Algebraic Solution for Discrete Tomography
TLDR
This chapter shows how the limited-angle tomography problem can be recast in a purely algebraic form, and presents an explicit formula for reconstructing a finite-support object from a finite number of its discrete projections over a limited range of angles. Expand
Discrete tomography by convex – concave regularization and D . C . programming
We present a novel approach to the tomographic reconstruction of binary objects from few projection directions within a limited range of angles. A quadratic objective functional over binary variablesExpand
A Novel Convex Relaxation for Non-binary Discrete Tomography
TLDR
This work presents a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements, with superior solutions both mathematically and experimentally in comparison to previously proposed relaxations. Expand
Reconstruction of Binary Images via the EM Algorithm
The problem of reconstructing a binary function x defined on a finite subset of a lattice ℤ, from an arbitrary collection of its partial sums is considered. The approach is based on (a) relaxing theExpand
Binary Tomography for Triplane Cardiography
TLDR
This hypothesis is experimentally validated for the Specific case of a class of binary images representing cardiac cross-sections, where the probability of the occurrence of a particular image of the class is determined by a Gibbs distribution and reconstruction is to be done from the three noisy projections. Expand
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
  • A. Chambolle, T. Pock
  • Computer Science, Mathematics
  • Journal of Mathematical Imaging and Vision
  • 2010
TLDR
A first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure can achieve O(1/N2) convergence on problems, where the primal or the dual objective is uniformly convex, and it can show linear convergence, i.e. O(ωN) for some ω∈(0,1), on smooth problems. Expand
DART: A Practical Reconstruction Algorithm for Discrete Tomography
TLDR
An iterative reconstruction algorithm for discrete tomography, called discrete algebraic reconstruction technique (DART), which is capable of computing more accurate reconstructions from a small number of projection images, or from asmall angular range, than alternative methods. Expand
Advances in discrete tomography and its applications
ANHA Series Preface Preface List of Contributors Introduction / A. Kuba and G.T. Herman Part I. Foundations of Discrete Tomography An Introduction to Discrete Point X-Rays / P. Dulio, R.J. Gardner,Expand
A Convex Programming Algorithm for Noisy Discrete Tomography
A convex programming approach to discrete tomographic image reconstruction in noisy environments is proposed. Conventional constraints are mixed with noise-based constraints on the sinogram and aExpand
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