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MURI Research Publications

MURI Research Publications

  • "Anisotropic Smoothness Spaces via Level Sets", Ronald DeVore, Guergana Petrova, Przemysław Wojtaszczyk; will appear in Communications in Pure and Applied Mathematics.

    It has been understood for some time that the classical smoothness spaces, such as the Sobolev and Besov classes, are not satisfactory for certain problems in image processing and nonlinear PDEs... [more]

  • "Greedy Wavelet Projections are Bounded on BV", Paweł Bechler, Ronald DeVore, Anna Kamont, Guergana Petrova, Przemysław Wojtaszczyk, Trans. Amer. Math. Soc., 359 (2007), 637--648.

    Let BV = BV(IRd) be the space of functions of bounded variation on IRd with d ≥ 2. Let Ψλ, λ ∈ Δ, be a wavelet system of compactly supported functions normalized in BV, i.e... [more]

  • "Random Projections of Smooth Manifolds", Richard G. Baraniuk, Michael B. Wakin; to appear in Foundations of Computational Mathematics.

    We propose a new approach for nonadaptive dimensionality reduction of manifold-modeled data, demonstrating that a small number of random linear projections can preserve key information about a manifold-modeled signal... [more]

  • "The Smashed Filter for Compressive Classification and Target Recognition", Mark A. Davenport, Marco F. Duarte, Michael B. Wakin, Jason N. Laskar, Dharmpal Takhar, Kevin F. Kelly, Richard G. Baraniuk, Proc. of Computational Imaging V at SPIE Electronic Imaging, San Jose, California, January 2007.

    The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible image or signal from a small set of linear, non-adaptive (even random) projections. However, in many applications... [more]

  • "A Simple Proof of the Restricted Isometry Property for Random Matrices", Richard Baraniuk, Mark Davenport, Ronald DeVore, Michael Wakin; to appear in Constructive Approximation.

    We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients... [more]

  • "High-Resolution Navigation on Non-Differentiable Image Manifolds", Michael B. Wakin, David L. Donoho, Hyeokho Choi, and Richard G. Baraniuk, IEEE 2005 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 2005, Philadelphia, Pennsylvania, March 2005.

    The images generated by varying the underlying articulation parameters of an object (pose, attitude, light source position, and so on) can be viewed as points... [more]

  • "Wavelet-Domain Approximation and Compression of Piecewise Smooth Images", Michael B. Wakin, Justin K. Romberg, Hyeokho Choi, Richard G. Baraniuk, IEEE Transactions on Image Processing, Vol. 15, No. 5, May 2006.

    The wavelet transform provides a sparse representation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees... [more]

  • "Adaptive Approximation of Curves", Peter Binev, Wolfgang Dahmen, Ronald DeVore, Nira Dyn.

    We propose adaptive multiscale refinement algorithms for approximating and encoding curves by polygonal curves. We establish rates of approximation of these algorithms... [more]

  • "A fast sweeping method for static convex Hamilton-Jacobi equations", Jianliang Qian, Yong-Tao Zhang, Hong-Kai Zhao, Journal of Scientific Computing, Vol. 31, No. 1/2, pp. 237-271, 2007.

    We develop a fast sweeping method for static Hamilton-Jacobi equations with convex Hamiltonians. Local solvers and fast sweeping strategies apply to structured and unstructured meshes... [more]

  • "A Direct Imaging Algorithm For Extended Targets", S. Hou, K. Solna, H. Zhao, Inverse Problem, Vol. 22, 1151-1178, 2006.

    We present a direct imaging algorithm for extended targets. The algorithm is based on a physical factorization of the response matrix of a transducer array... [more]

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