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Compressive sensing
 IEEE Signal Processing Mag
, 2007
"... The Shannon/Nyquist sampling theorem tells us that in order to not lose information when uniformly sampling a signal we must sample at least two times faster than its bandwidth. In many applications, including digital image and video cameras, the Nyquist rate can be so high that we end up with too m ..."
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Cited by 696 (62 self)
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will learn about a new technique that tackles these issues using compressive sensing [1, 2]. We will replace the conventional sampling and reconstruction operations with a more general linear measurement scheme coupled with an optimization in order to acquire certain kinds of signals at a rate significantly
High performance scalable image compression with EBCOT
 IEEE Trans. Image Processing
, 2000
"... A new image compression algorithm is proposed, based on independent Embedded Block Coding with Optimized Truncation of the embedded bitstreams (EBCOT). The algorithm exhibits stateoftheart compression performance while producing a bitstream with a rich feature set, including resolution and SNR ..."
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Cited by 586 (11 self)
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A new image compression algorithm is proposed, based on independent Embedded Block Coding with Optimized Truncation of the embedded bitstreams (EBCOT). The algorithm exhibits stateoftheart compression performance while producing a bitstream with a rich feature set, including resolution and SNR
A Simple Proof of the Restricted Isometry Property for Random Matrices
 CONSTR APPROX
, 2008
"... 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: (i) concentration inequalities for random inner products that have recently provided algorithmical ..."
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Cited by 631 (64 self)
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, we obtain simple and direct proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) and proofs of the existence of optimal Compressed Sensing measurement matrices. In the process, we also prove that these measurements have a certain
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 873 (26 self)
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by solving a simple convex optimization program. This program finds the matrix with minimum nuclear norm that fits the data. The condition above assumes that the rank is not too large. However, if one replaces the 1.2 exponent with 1.25, then the result holds for all values of the rank. Similar results hold
On the optimal compression of sets in PSPACE
"... We show that if DTIME[2 O(n) ] is not included in DSPACE[2 o(n)], then, for every set B in PSPACE, all strings x in B of length n can be represented by a string compressed(x) of length at most log(B =n ) + O(log n), such that a polynomialtime algorithm, given compressed(x), can distinguish x fro ..."
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We show that if DTIME[2 O(n) ] is not included in DSPACE[2 o(n)], then, for every set B in PSPACE, all strings x in B of length n can be represented by a string compressed(x) of length at most log(B =n ) + O(log n), such that a polynomialtime algorithm, given compressed(x), can distinguish x
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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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 power
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 770 (13 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
Optimal Compression of Traffic Flow Data
"... Experimental characterization of complex physical laws by probability density function of measured data is treated. For this purpose we introduce a statistical Gaussian mixture model comprised of representative data and probabilities related to them. To develop an algorithm for adaptation of represe ..."
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a particular day at an observation point is described by a vector comprised of 24 components. The set of 365 vectors measured in one year is optimally compressed to just 4 representative vectors and related probabilities. These vectors represent the flow rate in normal working days and weekends
Progressive Meshes
"... Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new s ..."
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Cited by 1315 (11 self)
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scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuousresolution representation addresses several practical problems in graphics: smooth geomorphing of levelofdetail approximations, progressive transmission, mesh compression, and selective refinement
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
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Cited by 562 (20 self)
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for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds
Results 1  10
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