Browsing by Author "Yin, W."
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Item A Linearized Bregman Algorithm for Decentralized Basis Pursuit(2013-04) Yuan, K.; Ling, Q.; Yin, W.; Ribeiro, A.We solve a decentralized basis pursuit problem in a multiagent system, where each agent holds part of the linear observations on a common sparse vector, and all the agents collaborate to recover the sparse vector through limited neighbor-to-neighbor communication. The proposed decentralized linearized Bregman algorithm solves the Lagrange dual of an augmented l1 model that is equivalent to basis pursuit. The fact that this dual problem is unconstrained and differentiable enables a lightweight yet efficient decentralized gradient algorithm. We prove nearly linear convergence of the algorithm in the sense that uniformly for every agent i, the error obeys |x_i(k) - x*|<=e(k) and e(k)<=rho e(k-1)+gamma, where rho<=1 and gamma>=0 are independent of k or i. Numerical experiments demonstrate this convergence.Item A New Regularization Path for Logistic Regression via Linearized Bregman(2012-10) Shi, J.V.; Yin, W.; Osher, S.J.Sparse logistic regression is an important linear classifier in statistical learning, providing an attractive route for feature selection. A popular approach is based on minimizing an l1-regularization term with a regularization parameter lambda that affects the solution sparsity. To determine an appropriate value for the regularization parameter, one can apply the grid search method or the Bayesian approach. The grid search method requires constructing a regularization path, by solving a sequence of minimization problems with varying values of the regularization parameter, which is typically time consuming. In this paper, we introduce a fast procedure that generates a new regularization path without tuning the regularization parameter. We first derive the direct Bregman method by replacing the l1-norm by its Bregman divergence, and contrast it with the grid search method. For faster path computation, we further derive the linearized Bregman algorithm, which is algebraically simple and computationally efficient. Finally we demonstrate some empirical results for the linearized Bregman algorithm on benchmark data and study feature selection as an inverse problem. Compared with the grid search method, the linearized Bregman algorithm generates a different regularization path with comparable classification performance, in a much more computationally efficient manner.Item An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise(2008-08) Yang, J.; Zhang, Y.; Yin, W.We extend the alternating minimization algorithm recently proposed in [38, 39] to the case of recovering blurry multichannel (color) images corrupted by impulsive rather than Gaussian noise. The algorithm minimizes the sum of a multichannel extension of total variation (TV), either isotropic or anisotropic, and a data fidelity term measured in the L1-norm. We derive the algorithm by applying the well-known quadratic penalty function technique and prove attractive convergence properties including finite convergence for some variables and global q-linear convergence. Under periodic boundary conditions, the main computational requirements of the algorithm are fast Fourier transforms and a low-complexity Gaussian elimination procedure. Numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm. In addition, it is numerically compared to an algorithm recently proposed in [20] that uses a linear program and an interior point method for recovering grayscale images.Item Extracting Respiratory Signals from Thoracic Cone Beam CT Projections(2012-10) Yan, H.; Wang, X.; Yin, W.; Pan, T.; Ahmad, M.; Mou, X.; Cervino, L.; Jia, X.; Jiang, S.B.Patient respiratory signal associated with the cone beam CT (CBCT) projections is important for lung cancer radiotherapy. In contrast to monitoring an external surrogate of respiration, such signal can be extracted directly from the CBCT projections. In this paper, we propose a novel local principle component analysis (LPCA) method to extract the respiratory signal by distinguishing the respiration motion-induced content change 25 from the gantry rotation-induced content change in the CBCT projections. The LPCA method is evaluated by comparing with three state-of-the-art projection-based methods, namely, the Amsterdam Shroud (AS) method, the intensity analysis (IA) method, and the Fourier-transform based phase analysis (FT-p) method. The clinical CBCT projection data of eight patients, acquired under various clinical scenarios, were used to investigate 30 the performance of each method. We found that the proposed LPCA method has demonstrated the best overall performance for cases tested and thus is a promising technique for extracting respiratory signal. We also identified the applicability of each existing method.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 Linearly Convergent Decentralized Consensus Optimization with the Alternating Direction Method of Multipliers(2013-04) Shi, W.; Ling, Q.; Yuan, K.; Wu, G.; Yin, W.In a decentralized consensus optimization problem, a network of agents minimizes the summation of their local objective functions on a common set of decision variables, allowing only information exchange among neighbors. The alternating direction method of multipliers (ADMM) has been shown to be a powerful tool for solving the problem with empirically fast convergence. This paper establishes the linear convergence rate of the ADMM in decentralized consensus optimization. The theoretical convergence rate is a function of the network topology, properties of the local objective functions, and the algorithm parameter. This result not only gives a performance guarantee for the ADMM but also provides a guideline to accelerate its convergence for decentralized consensus optimization problems.Item Opportunistic Sensing: Unattended Acoustic Sensor Selection using Crowdsourcing Models(2012-08) Huang, P.-S.; Hasegawa-Johnson, M.; Yin, W.; Huang, T.S.Unattended wireless sensor networks have been widely used in many applications. This paper proposes automatic sensor selection methods based on crowdsourcing models in the Opportunistic Sensing framework, with applications to unattended acoustic sensor selection. Precisely, we propose two sensor selection criteria and solve them via greedy algorithm and quadratic assignment. Our proposed method achieves, on average, 5.64% higher accuracy than the traditional approach under sparse reliability conditions.Item Signal Representation with Minimum L_Infinity Norm(2012-10) Studer, C.; Yin, W.; Baraniuk, R.G.Maximum (or L_infinity) norm minimization subject to an underdetermined system of linear equations finds use in a large number of practical applications, such as vector quantization, peak-to-average power ratio (PAPR) (or "crest factor") reduction in wireless communication systems, approximate neighbor search, robotics, and control. In this paper, we analyze the fundamental properties of signal representations with minimum L_infinity-norm. In particular, we develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, 2010, and we characterize the limits of l_infinity-norm-based PAPR reduction. Our results show that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the effcient computation of so-called democratic representations, which have both provably small l_infinity-norm and low PAPR.