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Imaging From Sparse Measurements
, 2010
"... SUMMARY We consider the problem of using scattered waves to recover an image of the medium in which the waves propagate. We address the case of scalar waves when the sources and receivers are sparse and irregularly spaced. Our approach is based on the singlescattering (Born) approximation and the ..."
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and the generalized Radon transform. The key to handling sparse sources and receivers is the development of a dataweighting scheme that compensates for nonuniform sampling. To determine the appropriate weights, we formulate a criterion for measuring the optimality of the pointspread function, and solve
HIGHLY SPARSE REPRESENTATIONS FROM DICTIONARIES ARE UNIQUE AND INDEPENDENT OF THE SPARSENESS MEASURE
, 2003
"... Highly sparse representations from dictionaries are unique and independent of the sparseness measure ..."
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Highly sparse representations from dictionaries are unique and independent of the sparseness measure
Stable Signal Recovery from Incomplete and Inaccurate Measurements
, 2006
"... Suppose we wish to recover a vector x0 ∈ Rm (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x0 accurately based on the data y? To recover x0, we ..."
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Cited by 1363 (38 self)
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, we consider the solution x to the 1regularization problem min ‖x‖1 subject to ‖Ax − y‖2 ≤ , where is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the vector x0 is sufficiently sparse, then the solution is within the noise
Sparse Measurement Systems: Applications, Analysis, Algorithms and Design
"... This thesis deals with ‘largescale ’ detection problems that arise in many real world applications such as sensor networks, mapping with mobile robots and group testing for biological screening and drug discovery. These are problems where the values of a large number of inputs need to be inferred f ..."
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Cited by 1 (0 self)
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from noisy observations and where the transformation from input to measurement occurs because of a physical process. In particular, we focus on sparse measurement systems. We use the term sparse measurement system to refer to applications where every observation is a (stochastic) function of a small
Highly sparse representations from dictionaries are unique and independent of the sparseness measure
, 2003
"... ..."
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 1485 (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
An Architecture for WideArea Multicast Routing
"... Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets or ..."
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Cited by 530 (22 self)
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Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets
Compressed sensing
, 2004
"... We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal numbe ..."
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Cited by 3559 (22 self)
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We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal
Local features and kernels for classification of texture and object categories: a comprehensive study
 International Journal of Computer Vision
, 2007
"... Recently, methods based on local image features have shown promise for texture and object recognition tasks. This paper presents a largescale evaluation of an approach that represents images as distributions (signatures or histograms) of features extracted from a sparse set of keypoint locations an ..."
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Cited by 643 (34 self)
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Recently, methods based on local image features have shown promise for texture and object recognition tasks. This paper presents a largescale evaluation of an approach that represents images as distributions (signatures or histograms) of features extracted from a sparse set of keypoint locations
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 552 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Results 1  10
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