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Image Understanding using Sparse Representations

Published on Apr 1, 2014
Jayaraman J. Thiagarajan16
Estimated H-index: 16
(LLNL: Lawrence Livermore National Laboratory),
Karthikeyan Natesan Ramamurthy14
Estimated H-index: 14
(IBM)
+ 1 AuthorsAndreas Spanias29
Estimated H-index: 29
Abstract
Image understanding has been playing an increasingly crucial role in several inverse problems and computer vision. Sparse models form an important component in image understanding, since they emulate the activity of neural receptors in the primary visual cortex of the human brain. Sparse methods have been utilized in several learning problems because of their ability to provide parsimonious, interpretable, and efficient models. Exploiting the sparsity of natural signals has led to advances in several application areas including image compression, denoising, inpainting, compressed sensing, blind source separation, super-resolution, and classification. The primary goal of this book is to present the theory and algorithmic considerations in using sparse models for image understanding and computer vision applications. To this end, algorithms for obtaining sparse representations and their performance guarantees are discussed in the initial chapters. Furthermore, approaches for designing overcomplete, data-adapted dictionaries to model natural images are described. The development of theory behind dictionary learning involves exploring its connection to unsupervised clustering and analyzing its generalization characteristics using principles from statistical learning theory. An exciting application area that has benefited extensively from the theory of sparse representations is compressed sensing of image and video data. Theory and algorithms pertinent to measurement design, recovery, and model-based compressed sensing are presented. The paradigm of sparse models, when suitably integrated with powerful machine learning frameworks, can lead to advances in computer vision applications such as object recognition, clustering, segmentation, and activity recognition. Frameworks that enhance the performance of sparse models in such applications by imposing constraints based on the prior discriminatory information and the underlying geometrical structure, and kernelizing the sparse coding and dictionary learning methods are presented. In addition to presenting theoretical fundamentals in sparse learning, this book provides a platform for interested readers to explore the vastly growing application domains of sparse representations.
  • References (124)
  • Citations (14)
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References124
Newest
#1Karthikeyan Natesan Ramamurthy (ASU: Arizona State University)H-Index: 14
#2Jayaraman J. Thiagarajan (ASU: Arizona State University)H-Index: 16
Last. Andreas Spanias (ASU: Arizona State University)H-Index: 29
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The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we develop the paradigm of combined sparse representations, where only a part of the coefficient vector is constrained to be non-negative, and the rest is unconstrained (general). We anal...
4 CitationsSource
Nov 11, 2012 in BIBE (Bioinformatics and Bioengineering)
#1Jayaraman J. Thiagarajan (ASU: Arizona State University)H-Index: 16
#2Deepta Rajan (ASU: Arizona State University)H-Index: 5
Last. Andreas Spanias (ASU: Arizona State University)H-Index: 29
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In this paper, we describe a pixel based approach for automated segmentation of tumor components from MR images. Sparse coding with data-adapted dictionaries has been successfully employed in several image recovery and vision problems. Since it is trivial to obtain sparse codes for pixel values, we propose to consider their non-linear similarities to perform kernel sparse coding in a high dimensional feature space. We develop the kernel K-lines clustering procedure for inferring kernel dictionar...
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#1Karthikeyan Natesan Ramamurthy (ASU: Arizona State University)H-Index: 14
#2Jayaraman J. Thiagarajan (ASU: Arizona State University)H-Index: 16
Last. Andreas Spanias (ASU: Arizona State University)H-Index: 29
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Several supervised, semi-supervised, and unsupervised machine learning schemes can be unified under the general framework of graph embedding. Incorporating graph embedding principles into sparse representation based learning schemes can provide an improved performance in several learning tasks. In this work, we propose a dictionary learning procedure for computing discriminative sparse codes that obey graph embedding constraints. In order to compute the graph-embedded sparse codes, we integrate ...
11 CitationsSource
Sep 1, 2012 in ICIP (International Conference on Image Processing)
#1Kuldeep Kulkarni (ASU: Arizona State University)H-Index: 8
#2Pavan Turaga (ASU: Arizona State University)H-Index: 26
Recent advances in camera architectures and associated mathematical representations now enable compressive acquisition of images and videos at low data-rates. In such a setting, we consider the problem of human activity recognition, which is an important inference problem in many security and surveillance applications. We propose a framework for understanding human activities as a non-linear dynamical system, and propose a robust, generalizable feature that can be extracted directly from the com...
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Mar 25, 2012 in ICASSP (International Conference on Acoustics, Speech, and Signal Processing)
#1Hien Van Nguyen (UMD: University of Maryland, College Park)H-Index: 17
#2Vishal M. Patel (UMD: University of Maryland, College Park)H-Index: 44
Last. Rama Chellappa (UMD: University of Maryland, College Park)H-Index: 98
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In this paper, we present dictionary learning methods for sparse and redundant signal representations in high dimensional feature space. Using the kernel method, we describe how the well-known dictionary learning approaches such as the method of optimal directions and K-SVD can be made nonlinear. We analyze these constructions and demonstrate their improved performance through several experiments on classification problems. It is shown that nonlinear dictionary learning approaches can provide be...
88 CitationsSource
Dec 29, 2011 in ICIP (International Conference on Image Processing)
#1Karthikeyan Natesan Ramamurthy (ASU: Arizona State University)H-Index: 14
#2Jayaraman J. Thiagarajan (ASU: Arizona State University)H-Index: 16
Last. Andreas Spanias (ASU: Arizona State University)H-Index: 29
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Sparse representations using predefined and learned dictionaries have widespread applications in signal and image processing. Sparse approximation techniques can be used to recover data from its low dimensional corrupted observations, based on the knowledge that the data is sparsely representable using a known dictionary. In this paper, we propose a method to improve data recovery by ensuring that the data recovered using sparse approximation is close its manifold. This is achieved by performing...
10 CitationsSource
#1Jayaraman J. Thiagarajan (ASU: Arizona State University)H-Index: 16
#2Andreas Spanias (ASU: Arizona State University)H-Index: 29
Low dimensional embedding of data samples lying on a manifold can be performed using locally linear modeling. By incorporating suitable locality constraints, sparse coding can be adapted to modeling local regions of a manifold. This has been coupled with the spatial pyramid matching algorithm to achieve state-of-the-art performance in object recognition. In this paper, we propose an algorithm to learn dictionaries for computing local sparse codes of descriptors extracted from image patches. The ...
12 CitationsSource
#1Jort F. Gemmeke (Radboud University Nijmegen)H-Index: 19
#2Tuomas Virtanen (TUT: Tampere University of Technology)H-Index: 44
Last. Antti Hurmalainen (TUT: Tampere University of Technology)H-Index: 12
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This paper proposes to use exemplar-based sparse representations for noise robust automatic speech recognition. First, we describe how speech can be modeled as a linear combination of a small number of exemplars from a large speech exemplar dictionary. The exemplars are time-frequency patches of real speech, each spanning multiple time frames. We then propose to model speech corrupted by additive noise as a linear combination of noise and speech exemplars, and we derive an algorithm for recoveri...
303 CitationsSource
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K-hyperline clustering is an iterative algorithm based on singular value decomposition and it has been successfully used in sparse component analysis. In this paper, we prove that the algorithm converges to a locally optimal solution for a given set of training data, based on Lloyd's optimality conditions. Furthermore, the local optimality is shown by developing an Expectation-Maximization procedure for learning dictionaries to be used in sparse representations and by deriving the clustering alg...
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Jun 20, 2011 in CVPR (Computer Vision and Pattern Recognition)
#1Ran He (CAS: Chinese Academy of Sciences)H-Index: 34
#2Wei-Shi Zheng (SYSU: Sun Yat-sen University)H-Index: 41
Last. Xiangwei Kong (DUT: Dalian University of Technology)H-Index: 4
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An informative and discriminative graph plays an important role in the graph-based semi-supervised learning methods. This paper introduces a nonnegative sparse algorithm and its approximated algorithm based on the l0–l1 equivalence theory to compute the nonnegative sparse weights of a graph. Hence, the sparse probability graph (SPG) is termed for representing the proposed method. The nonnegative sparse weights in the graph naturally serve as clustering indicators, benefiting for semi-supervised ...
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Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional embeddings, they produce feature spaces that are hard to interpret. Further, in applications such as sensor design, one needs to perform reduction directly in the input domain, instead of constructing transformed spaces. Consequently, dimension selection (DS) aims to...
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Modeling data is the way we-scientists-believe that information should be explained and handled. Indeed, models play a central role in practically every task in signal and image processing and machine learning. Sparse representation theory (we shall refer to it as Sparseland) puts forward an emerging, highly effective, and universal model. Its core idea is the description of data as a linear combination of few atoms taken from a dictionary of such fundamental elements.
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Solving inverse problems continues to be a challenge in a wide array of applications ranging from deblurring, image inpainting, source separation etc. Most existing techniques solve such inverse problems by either explicitly or implicitly finding the inverse of the model. The former class of techniques require explicit knowledge of the measurement process which can be unrealistic, and rely on strong analytical regularizers to constrain the solution space, which often do not generalize well. The ...
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Building highly nonlinear and nonparametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. These methods are particularly preferred in cases where the training data sizes are limited and when prior knowledge of the data similarities is available. Despite their usefulness, the...
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