Title :
Comparison of optimization techniques for regularized statistical reconstruction in X-ray tomography
Author :
Hamelin, Benoit ; Goussard, Yves ; Dussault, Jean-Pierre
Author_Institution :
Inst. de Genie Biomed., Ecole Polytech. de Montreal, Montréal, QC, Canada
Abstract :
Numerical efficiency and convergence are matters of importance for regularized statistical reconstruction in X-ray tomography. We propose a performance comparison of four numerical methods that fall into two categories: first, variants of the SPS framework, a modern take on expectation-maximization-type algorithms, that benefit from acceleration through ordered subset strategies and were developed specifically for tomographic reconstruction; second, Hessian-free general-purpose nonlinear solvers with bound constraints, used to minimize directly the regularized objective function. The comparison is established on a common target for the noise-to-resolution trade-off of the reconstructed images. The experiments show that while the ordered-subsets separable paraboloidal surrogate iteration variant is the fastest to reach the target, its nonconvergent nature precludes the use of a rigorous stopping rule. Conversely, the other three methods are convergent and can be stopped using a common criterion related to the noise-to-resolution target. Among convergent techniques, general purpose solvers achieve the highest efficiency.
Keywords :
computerised tomography; convergence; expectation-maximisation algorithm; image reconstruction; medical image processing; optimisation; statistical analysis; Hessian-free general-purpose nonlinear solvers; SPS framework; X-ray tomography; bound constraints; convergence; convergent techniques; expectation-maximization-type algorithms; noise-to-resolution target; noise-to-resolution trade-off; nonconvergent nature; numerical efficiency; optimization techniques; ordered-subsets separable paraboloidal surrogate iteration variant; reconstructed images; regularized objective function; regularized statistical reconstruction; rigorous stopping rule; tomographic reconstruction; Computed tomography; Convergence; Image reconstruction; Image resolution; Noise; Optimization; Reconstruction algorithms; X-ray tomography; expectation-maximization; nonlinear optimization; numerical methods; ordered subsets; regularized statistical reconstruction;
Conference_Titel :
Image Processing Theory Tools and Applications (IPTA), 2010 2nd International Conference on
Conference_Location :
Paris
Print_ISBN :
978-1-4244-7247-5
DOI :
10.1109/IPTA.2010.5586755