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In this paper, we propose a fast primal-dual algorithm for solving bilaterally constrained total variation minimization problems which subsume the bilaterally constrained total variation image deblurring model and the two-phase piecewise constant Mumford-Shah image segmentation model. The presence of the bilateral constraints makes the optimality conditions of the primal-dual problem semi-smooth which can be solved by a semi-smooth Newton’s method superlinearly. But the linear system to solve at each iteration is very large and difficult to precondition. Using a primal-dual active-set strategy, we reduce the linear system to a much smaller and better structured one so that it can be solved efficiently by conjugate gradient with an approximate inverse preconditioner. Locally superlinear convergence results are derived for the proposed algorithm. Numerical experiments are also provided for both deblurring and segmentation problems. In particular, for the deblurring problem, we show that the addition of the bilateral constraints to the total variation model improves the quality of the solutions. [ABSTRACT FROM AUTHOR]

In [10,14], circulant-type preconditioners have been proposed for ill-conditioned Hermitian Toeplitz systems that are generated by nonnegative continuous functions with a zero of even order. The proposed circulant preconditioners can be constructed without requiring explicit knowledge of the generating functions. It was shown that the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers and that all eigenvalues are uniformly bounded away from zero. Therefore the conjugate gradient method converges linearly when applied to solving the circulant preconditioned systems. In [10,14], it was claimed that this result can be the case where the generating functions have multiple zeros. The main aim of this paper is to give a complete convergence proof of the method in [10,14] for this class of generating functions. [ABSTRACT FROM AUTHOR]

In many applications, it is required to reconstruct a high-resolution image from multiple, undersampled and shifted noisy images. Using the regularization techniques such as the classical Tikhonov regularization and maximum a posteriori (MAP) procedure, a high-resolution image reconstruction algorithm is developed. Because of the blurring process, the boundary values of the low-resolution image are not completely determined by the original image inside the scene. This paper addresses how to use (i) the Neumann boundary condition on the image, i.e., we assume that the scene immediately outside is a reflection of the original scene at the boundary, and (ii) the preconditioned conjugate gradient method with cosine transform preconditioners to solve linear systems arising from the high-resolution image reconstruction with multisensors. The usefulness of the algorithm is demonstrated through simulated examples. [ABSTRACT FROM AUTHOR]

The ability to culture pathogenic organisms substantially enhances the quest for fundamental knowledge and the development of vaccines and drugs. Thus, the elaboration of a protocol for the in vitro cultivation of the erythrocytic stages of Plasmodium falciparum revolutionized research on this important parasite. However, for P. vivax, the most widely distributed and difficult to treat malaria parasite, a strict preference for reticulocytes thwarts efforts to maintain it in vitro. Cultivation of P. cynomolgi, a macaque-infecting species phylogenetically close to P. vivax, was briefly reported in the early 1980s, but not pursued further. Here, we define the conditions under which P. cynomolgi can be adapted to long term in vitro culture to yield parasites that share many of the morphological and phenotypic features of P. vivax. We further validate the potential of this culture system for high-throughput screening to prime and accelerate anti-P. vivax drug discovery efforts. Present understanding of Plasmodium vivax biology is hampered by its inability to grow in vitro. Here, the authors developed an in vitro culture of its simian counterpart, P. cynomolgi, which shares morphological and phenotypic similarities with P. vivax, initiating a new phase in vivax research. [ABSTRACT FROM AUTHOR]