A new ADMM algorithm for the Euclidean median and its application to robust patch regression

The Euclidean Median (EM) of a set of points $\Omega$ in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in $\Omega$. While there exits no closed-form expression for the EM, it can nevertheless be computed using iterative methods such as the Wieszfeld algorithm. The EM has classically been used as a robust estimator of centrality for multivariate data. It was recently demonstrated that the EM can be used to perform robust patch-based denoising of images by generalizing the popular Non-Local Means algorithm. In this paper, we propose a novel algorithm for computing the EM (and its box-constrained counterpart) using variable splitting and the method of augmented Lagrangian. The attractive feature of this approach is that the subproblems involved in the ADMM-based optimization of the augmented Lagrangian can be resolved using simple closed-form projections. The proposed ADMM solver is used for robust patch-based image denoising and is shown to exhibit faster convergence compared to an existing solver.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201

Controlled Flow of Spin-Entangled Electrons via Adiabatic Quantum Pumping

We propose a method to dynamically generate and control the flow of spin-entangled electrons, each belonging to a spin-singlet, by means of adiabatic quantum pumping. The pumping cycle functions by periodic time variation of localized two-body interactions. We develop a generalized approach to adiabatic quantum pumping as traditional methods based on scattering matrix in one dimension cannot be applied here. We specifically compute the flow of spin-entangled electrons within a Hubbard-like model of quantum dots, and discuss possible implementations and identify parameters that can be used to control the singlet flow.Comment: 4 pages, 3 figure

Transparent, Non-local, Species-selective Transport in an Optical Superlattice Containing Two Interacting Atom Species

In an optical superlattice of triple wells, containing two mutually interacting atom species in adjacent wells, we show that one species can be transported through the positions of the other species, yet avoiding significant overlap and direct interaction. The transfer protocol is optimized to be robust against missing atoms of either species in any lattice site, as well as against lattice fluctuations. The degree and the duration of the inter-species overlap during passage can be tuned, making possible controlled large-scale interaction-induced change of internal states.Comment: 7 pages and 5 figure