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Optimal Recovery and Extremum Theory
, 2001
"... Abstract. In this paper optimal recovery problems of linear functionals on classes of smooth and analytic functions on the basis of linear information are considered from the general viewpoint of extremum theory. A general result about the connection of optimal recovery method with Lagrange multipli ..."
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Abstract. In this paper optimal recovery problems of linear functionals on classes of smooth and analytic functions on the basis of linear information are considered from the general viewpoint of extremum theory. A general result about the connection of optimal recovery method with Lagrange
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a powerlaw), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
Optimal Recovery Approach to Image Interpolation,” in
 Proc. IEEE ICIP’01
, 2001
"... We consider the problem of image interpolation from an adaptive optimal recovery point of view. Many different standard interpolation approaches may be viewed through the prism of optimal recovery. In this paper we review some standard image interpolation methods and how they relate to optimal recov ..."
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Cited by 15 (1 self)
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We consider the problem of image interpolation from an adaptive optimal recovery point of view. Many different standard interpolation approaches may be viewed through the prism of optimal recovery. In this paper we review some standard image interpolation methods and how they relate to optimal
Adaptive, OptimalRecovery Image Interpolation
"... We consider the problem of image interpolation using adaptive optimal recovery. We adaptively estimate the local quadratic signal class of our image pixels. We then use optimal recovery to estimate the missing local samples based on this quadratic signal class. This approach tends preserve edges, in ..."
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We consider the problem of image interpolation using adaptive optimal recovery. We adaptively estimate the local quadratic signal class of our image pixels. We then use optimal recovery to estimate the missing local samples based on this quadratic signal class. This approach tends preserve edges
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
 California Institute of Technology, Pasadena
, 2008
"... Abstract. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery alg ..."
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Cited by 766 (12 self)
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Abstract. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery
Computing optimal recovery policies for financial markets
, 2010
"... Computing optimal recovery policies for financial markets ..."
Demosaicing using optimal recovery
 IEEE Trans. Image Process
, 2005
"... Color images in single chip digital cameras are obtained by interpolating mosaiced color samples. These samples are encoded in a single chip CCD by sampling the light after it passes through a color filter array (CFA) that contains different color filters (i.e. red, green, and blue) placed in some p ..."
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Cited by 25 (0 self)
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Color images in single chip digital cameras are obtained by interpolating mosaiced color samples. These samples are encoded in a single chip CCD by sampling the light after it passes through a color filter array (CFA) that contains different color filters (i.e. red, green, and blue) placed in some pattern. The resulting sparsely sampled images of the threecolor planes are interpolated to obtain the complete color image. Interpolation usually introduces color artifacts due to the phaseshifted, aliased signals introduced by the sparse sampling of the CFAs. This paper introduces a nonlinear interpolation scheme based on edge information that produces high quality visual results. The new method is especially good at reconstructing the image around edges, a place where the visual human system is most sensitive.
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 860 (27 self)
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We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can
ADAPTIVE, OPTIMALRECOVERY IMAGE INTERPOLATION
"... We consider the problem of image interpolation using adaptive optimal recovery. We adaptively estimate the local quadratic signal class of our image pixels. We then use optimal recovery to estimate the missing local samples based on this quadratic signal class. This approach tends preserve edges, in ..."
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We consider the problem of image interpolation using adaptive optimal recovery. We adaptively estimate the local quadratic signal class of our image pixels. We then use optimal recovery to estimate the missing local samples based on this quadratic signal class. This approach tends preserve edges
The NewReno Modification to TCP’s Fast Recovery Algorithm", RFC 3782
, 2004
"... This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards " (STD 1) for the standardization state and status of this pro ..."
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Cited by 587 (10 self)
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of this protocol. Distribution of this memo is unlimited. Copyright Notice Copyright (C) The Internet Society (2004). All Rights Reserved. The purpose of this document is to advance NewReno TCP’s Fast Retransmit and Fast Recovery algorithms in RFC 2582 from Experimental to Standards Track status. The main change
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