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Joseph Shtok

  1. Analysis of Basis Pursuit Via Capacity Sets.

    Втр, 04/27/2010 - 15:02 — SomNambul
    Authors: Michael Elad, Joseph Shtok
    Subjects: Numerical Analysis
    Abstract

    Finding the sparsest solution $\alpha$ for an under-determined linear system
    of equations $D\alpha=s$ is of interest in many applications. This problem is
    known to be NP-hard. Recent work studied conditions on the support size of
    $\alpha$ that allow its recovery using L1-minimization, via the Basis Pursuit
    algorithm. These conditions are often relying on a scalar property of $D$
    called the mutual-coherence. In this work we introduce an alternative set of
    features of an arbitrarily given $D$, called the "capacity sets".

  2. Spatially-Adaptive Reconstruction in Computed Tomography Based on Statistical Learning.

    Втр, 04/27/2010 - 15:01 — SomNambul
    Authors: Michael Elad, Joseph Shtok, Michael Zibulevsky
    Subjects: Computer Vision and Pattern Recognition
    Abstract

    We propose a direct reconstruction algorithm for Computed Tomography, based
    on a local fusion of a few preliminary image estimates by means of a non-linear
    fusion rule. One such rule is based on a signal denoising technique which is
    spatially adaptive to the unknown local smoothness. Another, more powerful
    fusion rule, is based on a neural network trained off-line with a high-quality
    training set of images. Two types of linear reconstruction algorithms for the
    preliminary images are employed for two different reconstruction tasks.

Math-arch

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