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Computational methods for sparse solution of linear inverse problems
, 2009
"... The goal of sparse approximation problems is to represent a target signal approximately as a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, ..."
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The goal of sparse approximation problems is to represent a target signal approximately as a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a wealth of applications.
CodingBased System Primitives for Airborne Cloud Computing
, 2011
"... The recent proliferation of sensors in inhospitable environments such as disaster or battle zones has not been matched by in situ data processing capabilities due to a lack of computing infrastructure in the field. We envision a solution based on small, lowaltitude unmanned aerial vehicles (UAVs) t ..."
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The recent proliferation of sensors in inhospitable environments such as disaster or battle zones has not been matched by in situ data processing capabilities due to a lack of computing infrastructure in the field. We envision a solution based on small, lowaltitude unmanned aerial vehicles (UAVs) that can deploy elasticallyscalable computing infrastructure anywhere, at any time. This airborne compute cloud— essentially, microdata centers hosted on UAVs—would communicate with terrestrial assets over a bandwidthconstrained wireless network with variable, unpredictable link qualities. Achieving high performance over this groundtoair mobile radio channel thus requires making full and efficient use of every single transmission opportunity. To this end, this dissertation presents two system primitives that improve throughput and reduce network overhead by using recent distributed coding methods to exploit natural properties of the airborne environment (i.e., antenna beam diversity and anomaly sparsity).
Computer Vision and Image Understanding 117 (2013) 113–129 Contents lists available at SciVerse ScienceDirect Computer Vision and Image Understanding
"... journal homepage: www.elsevier.com/locate/cviu ..."
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Random Walks for Image Cosegmentation
, 2012
"... We recast the Cosegmentation problem using Random Walker (RW) segmentation as the core segmentation algorithm, rather than the traditional MRF approach adopted in the literature so far. Our formulation is similar to previous approaches in the sense that it also permits Cosegmentation constraints (w ..."
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We recast the Cosegmentation problem using Random Walker (RW) segmentation as the core segmentation algorithm, rather than the traditional MRF approach adopted in the literature so far. Our formulation is similar to previous approaches in the sense that it also permits Cosegmentation constraints (which impose consistency between the extracted objects from ≥ 2 images) using a nonparametric model. However, several previous nonparametric cosegmentation methods have the serious limitation that they require adding one auxiliary node (or variable) for every pair of pixels that are similar (which effectively limits such methods to describing only those objects that have high entropy appearance models). In contrast, our proposed model completely eliminates this restrictive dependence – the resulting improvements are quite significant. Our model further allows an optimization scheme exploiting quasiconvexity for modelbased segmentation with no dependence on the scale of the segmented foreground. Finally, we show that the optimization can be expressed in terms of linear algebra operations on sparse matrices which are easily mapped to GPU architecture. We provide a highly specialized CUDA library for Cosegmentation exploiting this special structure, and report experimental results showing these advantages. 1
Ph.D. Thesis Manifold Clustering for Motion Segmentation
"... I hereby declare that his thesis contains no material which has been accepted for the award of any other degree or diploma in any university. To the best of my knowledge and belief, this thesis contains no material previously published or written by another person, except where due reference has bee ..."
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I hereby declare that his thesis contains no material which has been accepted for the award of any other degree or diploma in any university. To the best of my knowledge and belief, this thesis contains no material previously published or written by another person, except where due reference has been made. In this study the problem of motion segmentation is discussed. Motion segmentation aims to decompose a video into the different objects that move throughout the sequence. In many computer vision algorithms this decomposition is the first fundamental step. It is an essential building block for robotics, inspection, video surveillance, video indexing, traffic monitoring and many other applications. The vast amount of literature on motion segmentation testifies to the relevance of the topic. However, the performance of most of the algorithms still falls far behind human perception. In this thesis a review of the main motion segmentation approaches is presented. The main features of motion segmentation algorithms are analysed and a classification of the recent and most important techniques is proposed.
Accelerated FirstOrder Stochastic Gradient Augmented Lagrangian
, 2011
"... Many applications need structured, approximate solutions of optimization formulations, rather than exact solutions. More Useful, More Credible Structured solutions are easier to understand. They correspond better to prior knowledge about the solution. They may be easier to use and actuate. Extract j ..."
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Many applications need structured, approximate solutions of optimization formulations, rather than exact solutions. More Useful, More Credible Structured solutions are easier to understand. They correspond better to prior knowledge about the solution. They may be easier to use and actuate. Extract just the essential meaning from the data set, not the less important effects. Less Data Needed Structured solution lies in lowerdimensional spaces ⇒ need to gather / sample less data to capture it. Choose good structure instead of “overfitting ” to a particular sample. The structural requirements have deep implications for how we formulate and solve these problems. Stephen Wright (UWMadison) Sparse Optimization SIAMOPT, May 2011 3 / 44ℓ1 and Sparsity A common type of desired structure is sparsity: We would like the approx solution x ∈ R n to have few nonzero components. A sparse formulation of “minx f (x) ” could be Find an approximate minimizer ¯x ∈ R n of f such that ‖x‖0 ≤ k, where ‖x‖0 denotes cardinality: the number of nonzeros in x. Too Hard! Use of ‖x‖1 has long been known to promote sparsity in x. Also, Can solve without discrete variables; It maintains convexity. Stephen Wright (UWMadison) Sparse Optimization SIAMOPT, May 2011 4 / 44Regularized Formulations with ℓ1
1Analog Sparse Approximation with Applications to Compressed Sensing
"... Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed dictionary. Unfortunately, inference in this model involves s ..."
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Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed dictionary. Unfortunately, inference in this model involves solving nonsmooth optimization problems that are computationally expensive. While significant efforts have focused on developing digital algorithms specifically for this problem, these algorithms are inappropriate for many applications because of the time and power requirements necessary to solve large optimization problems. Based on recent work in computational neuroscience, we explore the potential advantages of continuous time dynamical systems for solving sparse approximation problems if they were implemented in analog VLSI. Specifically, in the simulated task of recovering synthetic and MRI data acquired via compressive sensing techniques, we show that these systems can potentially perform recovery at time scales of 1020µs, supporting datarates of 50100 kHz (orders of magnitude faster that digital algorithms). Furthermore, we show analytically that a wide range of sparse approximation problems can be solved in the same basic architecture, including approximate `p norms, modified `1 norms, reweighted `1 and `2, the block `1 norm and classic Tikhonov regularization.