Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
The discrete Radon transform and its approximate inversion via linear programming
Discrete Applied Mathematics
Binary vectors partially determined by linear equation systems
Discrete Mathematics
Genetic algorithmic approach to the detection of subsurface voids in cross-hole seismic tomography
Pattern Recognition Letters
Reconstruction of convex 2D discrete sets in polynomial time
Theoretical Computer Science
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
Approximating Binary Images from Discrete X-Rays
SIAM Journal on Optimization
Reconstruction of hv-convex binary matrices from their absorbed projections
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Kaczmarz extended algorithm for tomographic image reconstruction from limited-data
Mathematics and Computers in Simulation
Discrete tomography by convex-concave regularization and D.C. programming
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
A sufficient condition for non-uniqueness in binary tomography with absorption
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Binary tomography by iterating linear programs from noisy projections
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Simulated annealing: Practice versus theory
Mathematical and Computer Modelling: An International Journal
ML parameter estimation for Markov random fields with applications to Bayesian tomography
IEEE Transactions on Image Processing
A generalized Gaussian image model for edge-preserving MAP estimation
IEEE Transactions on Image Processing
| Hi-index | 5.24 |
In this paper we discuss the selected image reconstruction methods of binary tomography in the context of their application to geophysical imaging. We restrict our considerations to a discrete version of high-frequency electromagnetic geotomography, which we label as Binary Electromagnetic Geotomography (BEG). Basically, such an imaging technique may be applied to detect subsurface anomalies (air-filled voids) whose attenuation coefficient is very low (nearly zero-value) and considerably different from that for the background. The assumption for a binary representation of the image to be reconstructed substantially relaxes image reconstruction problems related to ill-posedness that comes from an intrinsic limitation of an angular range of projections. We test two algorithms for binary tomography, where the penalty term is based on the Markov Random Field (MRF) model. The mean-field reference distribution and mean-field annealing are applied to estimate the global maximizer of the Gibbs-Boltzmann distribution associated with the objective function. We also apply the projected gradient algorithm that uses a binary steering. Very efficient implementations of the algorithms are also given. The numerical results are presented for noise-free, noisy, and real data.