Browsing by Author "Chen, Y."
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Item Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging(2011-09) Chen, Y.; Hager, W.W.; Huang, F.; Phan, D.T.; Ye, X.; Yin, W.This paper presents two fast algorithms for total variation-based image reconstruction in partially parallel magnetic resonance imaging (PPI) where the inversion matrix is large and ill-conditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more easily solved subproblems. The first method reduces the image reconstruction problem to an unconstrained minimization problem, which is solved by an alternating proximal minimization algorithm. One phase of the algorithm solves a total variation (TV) denoising problem, and second phase solves an ill-conditioned linear system. Linear and sublinear convergence results are given, and an implementation based on a primal-dual hybrid gradient (PDHG) scheme for the TV problem and a Barzilai-Borwein scheme for the linear inversion is proposed. The second algorithm exploits the special structure of the PPI reconstruction problem by decomposing it into one subproblem involving Fourier transforms and another subproblem that can be treated by the PDHG scheme. Numerical results and comparisons with recently developed methods indicate the efficiency of the proposed algorithms.Item Film drainage and the lifetime of bubbles(American Geophysical Union, 2013) Nguyen, C.T.; Gonnermann, H.M.; Chen, Y.[1] We present the results of new laboratory experiments that provide constraints on inter bubble film thinning and bubble coalescence as a consequence of liquid expulsion by gravitational and capillary forces. To ensure dynamic similarity to magmatic systems, the experiments are at small Reynolds numbers inline image and cover a wide range of Bond numbers (10−3 ≤ Bo ≤ 102). Results indicate that at Bo < 0.25 film drainage is due to capillary forces, whereas at Bo > 0.25 gravitational forces result in film thinning. The film drainage time scale is given by t ∼ C ln (α) τ and is orders of magnitude faster than often assumed for magmatic systems. Here, C ∼ 10 is an empirical constant and α is the ratio of initial film thickness to film thickness at the time of rupture and τ is the characteristic capillary or buoyancy time scale at values of Bo < 0.25 and Bo > 0.25, respectively.