## Sparse Representation For Computer Vision and Pattern Recognition (2009)

Citations: | 47 - 1 self |

### BibTeX

@MISC{Wright09sparserepresentation,

author = {John Wright and Yi Ma and Julien Mairal and Guillermo Sapiro and Thomas Huang and Shuicheng Yan},

title = {Sparse Representation For Computer Vision and Pattern Recognition},

year = {2009}

}

### OpenURL

### Abstract

Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on non-traditional applications where the goal is not just to obtain a compact high-fidelity 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 state-of-theart 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.

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Citation Context ...e the latter two methods are more directly suited for occlusion, as they produce lowerdimensional feature sets that are spatially localized. Figure 2 left also compares to the Nearest Subspace method =-=[45]-=-, which makes similar use of linear illumination models, but is not based on sparsity and does not correct sparse errors. The ℓ 1 -based approach achieves the highest overall recognition rate of the m... |

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Citation Context ...h several popular methods from the literature 3 : the Principal Component Analysis (PCA) approach of [67], Independent Component Analysis (ICA) [43], and Local Nonnegative Matrix Factorization (LNMF) =-=[46]-=-. The first provides a standard baseline of comparison, while the latter two methods are more directly suited for occlusion, as they produce lowerdimensional feature sets that are spatially localized.... |

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Citation Context ...of representing the actual data in terms of them, e.g., [17], [20], [30], have been developed in recent years, leading to state-ofthe-art results in many signal and image processing tasks [11], [32], =-=[44]-=-, [48], [51], [54]. We refer the reader to [10] for a recent review on the subject. The actual dictionary plays a critical role, and it has been shown again and again that learned and data adaptive di... |

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Citation Context ...se approaches have been extended for multiscale dictionaries and color images in [51], leading to state-of-the-art results. See Figure 4 for an example of color image denosing with this approach, and =-=[49]-=-, [51] for numerous additional examples, comparisons, and applications in image demosaicing, image inpainting, and image denoising. An example of a 5 The expression (11) can be derived from a MAP esti... |

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Citation Context ...the classification tasks introduced in the next section. In addition, these costs can be replaced by a (non-convex) Lorentzian penalty function, motivated either by further approximating the ℓ0 by ℓ1 =-=[15]-=-, or by considering a mixture of Laplacians prior for the coefficients in A and exploiting MDL concepts [55], instead of the more classical Laplacian prior. 5 Since (11) is not simultaneously convex i... |

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Citation Context ...e data samples [61]. Manifold learning algorithms such as ISOMAP [63], Locally Linear Embedding (LLE) [58], and Laplacian Eigenmaps (LE) [8], all rely on graphs constructed with different motivations =-=[73]-=-. Moreover, most popular subspace learning algorithms, e.g., Principal Component Analysis (PCA) [42] and Linear Discriminant Analysis (LDA) [7], can all be explained within the graph embedding framewo... |

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Citation Context ... the minimizer is uniquely defined. From the geometry of ℓ1-minimization, if (8) does not hold for some pair (α0, e0), then it does not hold for any (α, e) with the same signs and support as (α0, e0) =-=[23]-=-. Understanding ℓ1-recoverability at each (I, J, σ) completely characterizes which solutions to x = Dα + e can be correctly recovered. In this language, the following characterization of the error cor... |

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Citation Context ...University of Singapore. Address: Office E4-05-11, 4 Engineering Drive 3, 117576, Singapore. Email: eleyans@nus.edu.sg face recognition [71], image super-resolution [75], motion and data segmentation =-=[33]-=-, [56], supervised denoising and inpainting [51] and background modeling [16], [21] and image classification [47], [48]. In almost all of these applications, using sparsity as a prior leads to state-o... |

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Citation Context ...and Computer Engineering, National University of Singapore. Address: Office E4-05-11, 4 Engineering Drive 3, 117576, Singapore. Email: eleyans@nus.edu.sg face recognition [71], image super-resolution =-=[75]-=-, motion and data segmentation [33], [56], supervised denoising and inpainting [51] and background modeling [16], [21] and image classification [47], [48]. In almost all of these applications, using s... |

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Citation Context ...ses of the proposed framework include the optimization of the sensing matrix for a given dictionary as well as the optimization of the dictionary for a pre-defined sensing environment (see also [31], =-=[60]-=-, [69]). D. Learning to Sense As we have seen, learning overcomplete dictionaries that facilitate a sparse representation of the data as a liner combination of a few atoms from such dictionary leads t... |

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Citation Context ...ry for the task as well as the processing and acquisition pipeline. Sparse modeling, and in particular the (semi-) supervised case, can be considered as a non-linear extension of metric learning (see =-=[76]-=- for bibliography on the subject and [62] for details on the connections between sparse modeling and metric learning). Such interesting connection brings yet another exciting aspect into the ongoing s... |

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Citation Context ...1, 4 Engineering Drive 3, 117576, Singapore. Email: eleyans@nus.edu.sg face recognition [71], image super-resolution [75], motion and data segmentation [33], [56], supervised denoising and inpainting =-=[51]-=- and background modeling [16], [21] and image classification [47], [48]. In almost all of these applications, using sparsity as a prior leads to state-of-the-art results. The ability of sparse represe... |

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Citation Context ...ure 1, has a strong tendency to separate the identity of the face (red coefficients) from the error due to corruption or occlusion. Once the ℓ 1 -minimization problem has been solved (see, e.g., [9], =-=[26]-=-, [30]), classification (identifying the subject pictured) or validation (determining if the subject is present in the training database) can proceed by considering how strongly the recovered coeffici... |

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Citation Context ...number of observations, and we cannot directly solve for α0. However, under mild conditions [28], the desired solution (α0, e0) is 2 For a detailed explanation of how such images can be obtained, see =-=[68]-=-. Fig. 1. Overview of the face recognition approach. The method represents a test image (left), which is potentially occluded (top) or corrupted (bottom), as a sparse linear combination of all the tra... |

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Citation Context ...(11) consists of a quadratic fitting term and an ℓ0 or ℓ1 regularization term for each column of A, the balance of the two being defined by the penalty parameter λ (this parameter has been studied in =-=[35]-=-, [39], [55], [65], [79]). As mentioned above, the ℓ1 norm can be used as an approximation to ℓ0 , making the problem convex in A while still encouraging sparse solutions [64]. While for reconstructio... |

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Citation Context ...576, Singapore. Email: eleyans@nus.edu.sg face recognition [71], image super-resolution [75], motion and data segmentation [33], [56], supervised denoising and inpainting [51] and background modeling =-=[16]-=-, [21] and image classification [47], [48]. In almost all of these applications, using sparsity as a prior leads to state-of-the-art results. The ability of sparse representations to uncover semantic ... |

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Citation Context ...sity of Singapore. Address: Office E4-05-11, 4 Engineering Drive 3, 117576, Singapore. Email: eleyans@nus.edu.sg face recognition [71], image super-resolution [75], motion and data segmentation [33], =-=[56]-=-, supervised denoising and inpainting [51] and background modeling [16], [21] and image classification [47], [48]. In almost all of these applications, using sparsity as a prior leads to state-of-the-... |