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We study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise nonlinearity at each iteration to promote sparsity. In the high-dimensional limit, the joint empirical measure of the underlying sparse eigenvector and its estimate provided...
We provide a complete characterization of the randomized Kaczmarz algorithm (RKA) for inconsistent linear systems. The Kaczmarz algorithm, known in some fields as the algebraic reconstruction technique, is a classical method for solving large-scale overdetermined linear systems through a sequence of projection operators; the randomized Kaczmarz algorithm is a recent proposal by Strohmer and Vershynin...
The Kaczmarz method, or the algebraic reconstruction technique (ART), is a popular method for solving large-scale overdetermined systems of equations. Recently, Strohmer et al. proposed the randomized Kaczmarz algorithm, an improvement that guarantees exponential convergence to the solution. This has spurred much interest in the algorithm and its extensions. We provide in this paper an exact formula...
Joint processing of visible (RGB) and near-infrared (NIR) images has recently found some appealing applications, which make joint capturing a pair of visible and NIR images an important problem. In this paper, we propose a new method to design color filter arrays (CFA) and demosaicing matrices for acquiring NIR and visible images using a single sensor. The proposed method modifies the optimum CFA...
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