Results 1  10
of
490
Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
Abstract

Cited by 1492 (93 self)
 Add to MetaCart
A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
Robust face recognition via sparse representation,” (preprint
 IEEE Trans. Pattern Analysis and Machine Intelligence
"... Abstract — We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sp ..."
Abstract

Cited by 321 (22 self)
 Add to MetaCart
Abstract — We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by ℓ 1minimization, we propose a general classification algorithm for (imagebased) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as Eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly, by exploiting the fact that these errors are often sparse w.r.t. to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm, and corroborate the above claims.
Stable recovery of sparse overcomplete representations in the presence of noise
 IEEE TRANS. INFORM. THEORY
, 2006
"... Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes t ..."
Abstract

Cited by 291 (20 self)
 Add to MetaCart
Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further that the overcomplete system is incoherent, it is shown that the optimally sparse approximation to the noisy data differs from the optimally sparse decomposition of the ideal noiseless signal by at most a constant multiple of the noise level. As this optimalsparsity method requires heavy (combinatorial) computational effort, approximation algorithms are considered. It is shown that similar stability is also available using the basis and the matching pursuit algorithms. Furthermore, it is shown that these methods result in sparse approximation of the noisy data that contains only terms also appearing in the unique sparsest representation of the ideal noiseless sparse signal.
Independent Component Filters Of Natural Images Compared With Simple Cells In Primary Visual Cortex
, 1998
"... this article we investigate to what extent the statistical properties of natural images can be used to understand the variation of receptive field properties of simple cells in the mammalian primary visual cortex. The receptive fields of simple cells have been studied extensively (e.g., Hubel & Wies ..."
Abstract

Cited by 273 (0 self)
 Add to MetaCart
this article we investigate to what extent the statistical properties of natural images can be used to understand the variation of receptive field properties of simple cells in the mammalian primary visual cortex. The receptive fields of simple cells have been studied extensively (e.g., Hubel & Wiesel 1968, DeValois et al. 1982a, DeAngelis et al. 1993): they are localised in space and time, have bandpass characteristics in the spatial and temporal frequency domains, are oriented, and are often sensitive to the direction of motion of a stimulus. Here we will concentrate on the spatial properties of simple cells. Several hypotheses as to the function of these cells have been proposed. As the cells preferentially respond to oriented edges or lines, they can be viewed as edge or line detectors. Their joint localisation in both the spatial domain and the spatial frequency domain has led to the suggestion that they mimic Gabor filters, minimising uncertainty in both domains (Daugman 1980, Marcelja 1980). More recently, the match between the operations performed by simple cells and the wavelet transform has attracted attention (e.g., Field 1993). The approaches based on Gabor filters and wavelets basically consider processing by the visual cortex as a general image processing strategy, relatively independent of detailed assumptions about image statistics. On the other hand, the edge and line detector hypothesis is based on the intuitive notion that edges and lines are both abundant and important in images. This theme of relating simple cell properties with the statistics of natural images was explored extensively by Field (1987, 1994). He proposed that the cells are optimized specifically for coding natural images. He argued that one possibility for such a code, sparse coding...
Learning Overcomplete Representations
, 2000
"... In an overcomplete basis, the number of basis vectors is greater than the dimensionality of the input, and the representation of an input is not a unique combination of basis vectors. Overcomplete representations have been advocated because they have greater robustness in the presence of noise, can ..."
Abstract

Cited by 257 (11 self)
 Add to MetaCart
In an overcomplete basis, the number of basis vectors is greater than the dimensionality of the input, and the representation of an input is not a unique combination of basis vectors. Overcomplete representations have been advocated because they have greater robustness in the presence of noise, can be sparser, and can have greater flexibility in matching structure in the data. Overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex. Previous work has focused on finding the best representation of a signal using a fixed overcomplete basis (or dictionary). We present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data. We show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency. This can be viewed as a generalization of the technique of independent component analysis and provides a method for Bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures.
Fields of experts: A framework for learning image priors
 In CVPR
, 2005
"... We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhood ..."
Abstract

Cited by 229 (3 self)
 Add to MetaCart
We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhoods. Field potentials are modeled using a ProductsofExperts framework that exploits nonlinear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field of Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with and even outperform specialized techniques. 1.
Independent Factor Analysis
 Neural Computation
, 1999
"... We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square no ..."
Abstract

Cited by 219 (9 self)
 Add to MetaCart
We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing, but also the general case where the number of mixtures differs from the number of sources and the data are noisy. IFA is a twostep procedure. In the first step, the source densities, mixing matrix and noise covariance are estimated from the observed data by maximum likelihood. For this purpose we present an expectationmaximization (EM) algorithm, which performs unsupervised learning of an associated probabilistic model of the mixing situation. Each source in our model is described by a mixture of Gaussians, thus all the probabilistic calculations can be performed analytically. In the second step, the sources are reconstructed from the observed data by an optimal nonlinear ...
Efficient sparse coding algorithms
 In NIPS
, 2007
"... Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higherlevel features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we ..."
Abstract

Cited by 203 (12 self)
 Add to MetaCart
Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higherlevel features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we present efficient sparse coding algorithms that are based on iteratively solving two convex optimization problems: an L1regularized least squares problem and an L2constrained least squares problem. We propose novel algorithms to solve both of these optimization problems. Our algorithms result in a significant speedup for sparse coding, allowing us to learn larger sparse codes than possible with previously described algorithms. We apply these algorithms to natural images and demonstrate that the inferred sparse codes exhibit endstopping and nonclassical receptive field surround suppression and, therefore, may provide a partial explanation for these two phenomena in V1 neurons. 1
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinato ..."
Abstract

Cited by 202 (31 self)
 Add to MetaCart
A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easilyverifiable conditions under which optimallysparse solutions can be found by concrete, effective computational methods. Such theoretical results inspire a bold perspective on some important practical problems in signal and image processing. Several wellknown signal and image processing problems can be cast as demanding solutions of undetermined systems of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect. In this paper we review the theoretical results on sparse solutions of linear systems, empirical
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
, 2000
"... Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the M ..."
Abstract

Cited by 193 (32 self)
 Add to MetaCart
Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the Mdimensional source signal s(t). Many natural signals can be sparsely represented in a proper signal dictionary s i (t) = K X k=1 C ik ' k (t) (1.2) The scalar functions ' k