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- Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, Alan S. Willsky
- Foundations of Computational Mathematics
- 2012

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of… (More)

- Dmitry M. Malioutov, Müjdat Çetin, Alan S. Willsky
- IEEE Transactions on Signal Processing
- 2005

We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the /spl lscr//sub 1/-norm. A number of recent theoretical results on sparsifying properties of /spl lscr//sub 1/ penalties justify this… (More)

- Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Parrilo, Alan S. Willsky
- SIAM Journal on Optimization
- 2011

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this paper we consider a convex optimization… (More)

- Martin J. Wainwright, Tommi S. Jaakkola, Alan S. Willsky
- IEEE Transactions on Information Theory
- 2002

We introduce a new class of upper bounds on the log partition function of a Markov random field (MRF). This quantity plays an important role in various contexts, including approximating marginal distributions, parameter estimation, combinatorial enumeration, statistical decision theory, and large-deviations bounds. Our derivation is based on concepts from… (More)

- Andy Tsai, Anthony J. Yezzi, Alan S. Willsky
- IEEE Trans. Image Processing
- 2001

In this work, we first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah paradigm from a curve evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to… (More)

- Andy Tsai, Anthony J. Yezzi, +5 authors Alan S. Willsky
- IEEE Trans. Med. Imaging
- 2003

We propose a shape-based approach to curve evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras, we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance… (More)

- Erik B. Sudderth, Alexander T. Ihler, Michael Isard, William T. Freeman, Alan S. Willsky
- Commun. ACM
- 2003

Continuous quantities are ubiquitous in models of real-world phenomena, but are surprisingly difficult to reason about automatically. Probabilistic graphical models such as Bayesian networks and Markov random fields, and algorithms for approximate inference such as belief propagation (BP), have proven to be powerful tools in a wide range of applications in… (More)

- Martin J. Wainwright, Tommi S. Jaakkola, Alan S. Willsky
- IEEE Transactions on Information Theory
- 2005

We develop and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem… (More)

- Alexander T. Ihler, John W. Fisher, Randolph L. Moses, Alan S. Willsky
- IEEE Journal on Selected Areas in Communications
- 2005

— Automatic self-localization is a critical need for the effective use of ad-hoc sensor networks in military or civilian applications. In general, self-localization involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. distance measurements between sensors) over regions of the network. Furthermore,… (More)

- Martin J. Wainwright, Tommi S. Jaakkola, Alan S. Willsky
- IEEE Trans. Information Theory
- 2003

—We present a tree-based reparameterization (TRP) framework that provides a new conceptual view of a large class of algorithms for computing approximate marginals in graphs with cycles. This class includes the belief propagation (BP) or sum-product algorithm as well as variations and extensions of BP. Algorithms in this class can be formulated as a sequence… (More)