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936
Sparse subspace clustering
 In CVPR
, 2009
"... We propose a method based on sparse representation (SR) to cluster data drawn from multiple lowdimensional linear or affine subspaces embedded in a highdimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all oth ..."
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Cited by 241 (14 self)
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We propose a method based on sparse representation (SR) to cluster data drawn from multiple lowdimensional linear or affine subspaces embedded in a highdimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. Our key contribution is to show that, under mild assumptions, the SR can be obtained ’exactly ’ by using ℓ1 optimization. The segmentation of the data is obtained by applying spectral clustering to a similarity matrix built from this SR. Our method can handle noise, outliers as well as missing data. We apply our subspace clustering algorithm to the problem of segmenting multiple motions in video. Experiments on 167 video sequences show that our approach significantly outperforms stateoftheart methods. 1.
RASL: Robust Alignment by Sparse and Lowrank Decomposition for Linearly Correlated Images
, 2010
"... This paper studies the problem of simultaneously aligning a batch of linearly correlated images despite gross corruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of ..."
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Cited by 161 (6 self)
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This paper studies the problem of simultaneously aligning a batch of linearly correlated images despite gross corruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of errors and a lowrank matrix of recovered aligned images. We reduce this extremely challenging optimization problem to a sequence of convex programs that minimize the sum of ℓ1norm and nuclear norm of the two component matrices, which can be efficiently solved by scalable convex optimization techniques with guaranteed fast convergence. We verify the efficacy of the proposed robust alignment algorithm with extensive experiments with both controlled and uncontrolled real data, demonstrating higher accuracy and efficiency than existing methods over a wide range of realistic misalignments and corruptions.
Sparse Representation For Computer Vision and Pattern Recognition
, 2009
"... Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact highfidelity representation of the observed signal, but also to extract semantic information. The choice of ..."
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Cited by 146 (9 self)
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Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact highfidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining stateoftheart results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.
Robust Subspace Segmentation by LowRank Representation
"... We propose lowrank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowestrank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlik ..."
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Cited by 145 (25 self)
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We propose lowrank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowestrank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlike the wellknown sparse representation (SR), which computes the sparsest representation of each data vector individually, LRR aims at finding the lowestrank representation of a collection of vectors jointly. LRR better captures the global structure of data, giving a more effective tool for robust subspace segmentation from corrupted data. Both theoretical and experimental results show that LRR is a promising tool for subspace segmentation. 1.
CurveletWavelet Regularized Split Bregman Iteration for Compressed Sensing
"... Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows to recover this signal from much fewer samples than the ShannonNyquist theory requires. Many images ..."
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Cited by 119 (6 self)
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Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows to recover this signal from much fewer samples than the ShannonNyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent pointlike features while curvelets represent linelike features well. For a suitable recovery of images, we propose models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = Φu + ɛ with the measurement matrix Φ ∈ R K×N, K<<N, we consider a jointly sparsityconstrained optimization problem of the form argmin{‖ΛcΨcu‖1 + ‖ΛwΨwu‖1 + u 1 2‖f − Φu‖22}. Here Ψcand Ψw are the transform matrices corresponding to the two frames, and the diagonal matrices Λc, Λw contain the weights for the frame coefficients. We present efficient iteration methods to solve the optimization problem, based on Alternating Split Bregman algorithms. The convergence of the proposed iteration schemes will be proved by showing that they can be understood as special cases of the DouglasRachford Split algorithm. Numerical experiments for compressed sensing based Fourierdomain random imaging show good performances of the proposed curveletwavelet regularized split Bregman (CWSpB) methods,whereweparticularlyuseacombination of wavelet and curvelet coefficients as sparsity constraints.
Towards a Practical Face Recognition System: Robust Alignment and Illumination by Sparse Representation
, 2010
"... Many classic and contemporary face recognition algorithms work well on public data sets, but degrade sharply when they are used in a real recognition system. This is mostly due to the difficulty of simultaneously handling variations in illumination, image misalignment, and occlusion in the test imag ..."
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Cited by 108 (10 self)
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Many classic and contemporary face recognition algorithms work well on public data sets, but degrade sharply when they are used in a real recognition system. This is mostly due to the difficulty of simultaneously handling variations in illumination, image misalignment, and occlusion in the test image. We consider a scenario where the training images are well controlled, and test images are only loosely controlled. We propose a conceptually simple face recognition system that achieves a high degree of robustness and stability to illumination variation, image misalignment, and partial occlusion. The system uses tools from sparse representation to align a test face image to a set of frontal training images. The region of attraction of our alignment algorithm is computed empirically for public face datasets such as MultiPIE. We demonstrate how to capture a set of training images with enough illumination variation that they span test images taken under uncontrolled illumination. In order to evaluate how our algorithms work under practical testing conditions, we have implemented a complete face recognition system, including a projectorbased training acquisition system. Our system can efficiently and effectively recognize faces under a variety of realistic conditions, using only frontal images under the proposed illuminations as training.
Sparse Representation or Collaborative Representation: Which Helps Face Recognition?
"... As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to th ..."
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Cited by 107 (16 self)
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As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l1norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC.
Discriminative KSVD for dictionary learning in face recognition
 In CVPR
"... In a sparserepresentationbased face recognition scheme, the desired dictionary should have good representational power (i.e., being able to span the subspace of all faces) while supporting optimal discrimination of the classes (i.e., different human subjects). We propose a method to learn an over ..."
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Cited by 105 (0 self)
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In a sparserepresentationbased face recognition scheme, the desired dictionary should have good representational power (i.e., being able to span the subspace of all faces) while supporting optimal discrimination of the classes (i.e., different human subjects). We propose a method to learn an overcomplete dictionary that attempts to simultaneously achieve the above two goals. The proposed method, discriminative KSVD (DKSVD), is based on extending the KSVD algorithm by incorporating the classification error into the objective function, thus allowing the performance of a linear classifier and the representational power of the dictionary being considered at the same time by the same optimization procedure. The DKSVD algorithm finds the dictionary and solves for the classifier using a procedure derived from the KSVD algorithm, which has proven efficiency and performance. This is in contrast to most existing work that relies on iteratively solving subproblems with the hope of achieving the global optimal through iterative approximation. We evaluate the proposed method using two commonlyused face databases, the Extended YaleB database and the AR database, with detailed comparison to 3 alternative approaches, including the leading stateoftheart in the literature. The experiments show that the proposed method outperforms these competing methods in most of the cases. Further, using Fisher criterion and dictionary incoherence, we also show that the learned dictionary and the corresponding classifier are indeed betterposed to support sparserepresentationbased recognition. 1.
Signal Processing with Compressive Measurements
, 2009
"... The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquistrate samples. Interestingly, it has been sh ..."
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Cited by 102 (25 self)
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The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquistrate samples. Interestingly, it has been shown that random projections are a nearoptimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems—such as detection, classification, or estimation—and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.