Gábor T. Herman

Elias S. Helou, Gabor T. Herman, Chuan Lin et al.

Properties of Superiorized Preconditioned Conjugate Gradient (SupPCG) algorithms in image reconstruction from projections are examined. Least squares (LS) is usually chosen for measuring data-inconsistency in these inverse problems. Preconditioned Conjugate Gradient algorithms are fast methods for finding an LS solution. However, for ill-posed problems, such as image reconstruction, an LS solution may not provide good image quality. This can be taken care of by superiorization. A superiorized algorithm leads to images with the value of a secondary criterion (a merit function such as the total variation) improved as compared to images with similar data-inconsistency obtained by the algorithm without superiorization. Numerical experimentation shows that SupPCG can lead to high-quality reconstructions within a remarkably short time. A theoretical analysis is also provided.

Marcelo V. W. Zibetti, Gabor T. Herman, Ravinder R. Regatte

Purpose: A fast data-driven optimization approach, named bias-accelerated subset selection (BASS), is proposed for learning efficacious sampling patterns (SPs) with the purpose of reducing scan time in large-dimensional parallel MRI. Methods: BASS is applicable when Cartesian fully-sampled k-space data of specific anatomy is available for training and the reconstruction method is specified, learning which k-space points are more relevant for the specific anatomy and reconstruction in recovering the non-sampled points. BASS was tested with four reconstruction methods for parallel MRI based on low-rankness and sparsity that allow a free choice of the SP. Two datasets were tested, one of the brain images for high-resolution imaging and another of knee images for quantitative mapping of the cartilage. Results: BASS, with its low computational cost and fast convergence, obtained SPs 100 times faster than the current best greedy approaches. Reconstruction quality increased up to 45\% with our learned SP over that provided by variable density and Poisson disk SPs, considering the same scan time. Optionally, the scan time can be nearly halved without loss of reconstruction quality. Conclusion: Compared with current approaches, BASS can be used to rapidly learn effective SPs for various reconstruction methods, using larger SP and larger datasets. This enables a better selection of efficacious sampling-reconstruction pairs for specific MRI problems.

Y. Censor, W. Chen, P. L. Combettes et al.

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of unknowns satisfying up to hundreds of thousands of constraints) and by a discussion of the demonstrated efficacy of projection methods in numerous scientific publications and commercial patents (dealing with problems that can have over a billion unknowns and a similar number of constraints).