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The "Independent Components" of Natural Scenes are Edge Filters
, 1997
"... It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attem ..."
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Cited by 477 (27 self)
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It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attempts to find a factorial code of independent visual features. We show here that a new unsupervised learning algorithm based on information maximization, a nonlinear "infomax" network, when applied to an ensemble of natural scenes produces sets of visual filters that are localized and oriented. Some of these filters are Gaborlike and resemble those produced by the sparsenessmaximization network. In addition, the outputs of these filters are as independent as possible, since this infomax network performs Independent Components Analysis or ICA, for sparse (supergaussian) component distributions. We compare the resulting ICA filters and their associated basis functions, with other decorrelating filters produced by Principal Components Analysis (PCA) and zerophase whitening filters (ZCA). The ICA filters have more sparsely distributed (kurtotic) outputs on natural scenes. They also resemble the receptive fields of simple cells in visual cortex, which suggests that these neurons form a natural, informationtheoretic
Survey of Sparse and NonSparse Methods in Source Separation
, 2005
"... Source separation arises in a variety of signal processing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sour ..."
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Cited by 35 (1 self)
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Source separation arises in a variety of signal processing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sources. When the information about the mixing process and sources is limited, the problem is called ‘blind’. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that solutions to previously problematic blind source separation problems can be obtained. In some cases, solutions are possible to problems intractable by previous nonsparse methods. Indeed, sparse methods provide a powerful approach to the separation of linear mixtures of independent data. This paper surveys the recent arrival of sparse blind source separation methods and the previously existing nonsparse methods, providing insights and appropriate hooks into the literature along the way.
Blind System Identification
, 1997
"... Blind system identification is a fundamental signal processing technology aimed to retrieve unknown information of a system from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation and blind image restoration. Th ..."
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Cited by 22 (1 self)
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Blind system identification is a fundamental signal processing technology aimed to retrieve unknown information of a system from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation and blind image restoration. This paper reviews a number of recently developed concepts and techniques for blind system identification which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the system's impulse response, and other techniques for direct estimation of the system input. Keywords: System identification, Blind techniques, Multichannels, Equalization, Source separation. This work has been supported by the Australian Research Council and the Australian Cooperative Research Center for Sensor Signal and Information Processing. y Currently with Motorola Australian Research Centre, 12 Lord Street, Botany 2019, ...
Compressive Sensing of Streams of Pulses
"... as an enticing alternative to the traditional process of signal acquisition. For a lengthN signal with sparsity K, merely M = O (K log N) ≪ N random linear projections (measurements) can be used for robust reconstruction in polynomial time. Sparsity is a powerful and simple signal model; yet, rich ..."
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Cited by 3 (2 self)
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as an enticing alternative to the traditional process of signal acquisition. For a lengthN signal with sparsity K, merely M = O (K log N) ≪ N random linear projections (measurements) can be used for robust reconstruction in polynomial time. Sparsity is a powerful and simple signal model; yet, richer models that impose additional structure on the sparse nonzeros of a signal have been studied theoretically and empirically from the CS perspective. In this work, we introduce and study a sparse signal model for streams of pulses, i.e., Ssparse signals convolved with an unknown Fsparse impulse response. Our contributions are threefold: (i) we geometrically model this set of signals as an infinite union of subspaces; (ii) we derive a sufficient number of random measurements M required to preserve the metric information of this set. In particular this number is linear merely in the number of degrees of freedom of the signal S + F, and sublinear in the sparsity K = SF; (iii) we develop an algorithm that performs recovery of the signal from M measurements and analyze its performance under noise and model mismatch. Numerical experiments on synthetic and real data demonstrate the utility of our proposed theory and algorithm. Our method is amenable to diverse applications such as the highresolution sampling of neuronal recordings and ultrawideband (UWB) signals. I.
Sampling and Recovery of Pulse Streams
"... Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the Ndimensional basis representation has just K ≪ N significant coefficients; in this case, the ..."
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Cited by 3 (1 self)
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Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the Ndimensional basis representation has just K ≪ N significant coefficients; in this case, the CS theory maintains that just M = O (K log N) random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to Ssparse signals/images that are convolved with an unknown Fsparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K = SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naive bound based on the total signal sparsity K = SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and
COMPRESSIVE SENSING OF A SUPERPOSITION OF PULSES
"... Compressive Sensing (CS) has emerged as a potentially viable technique for the efficient acquisition of highresolution signals and images that have a sparse representation in a fixed basis. The number of linear measurements M required for robust polynomial time recovery of Ssparse signals of lengt ..."
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Cited by 1 (1 self)
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Compressive Sensing (CS) has emerged as a potentially viable technique for the efficient acquisition of highresolution signals and images that have a sparse representation in a fixed basis. The number of linear measurements M required for robust polynomial time recovery of Ssparse signals of length N can be shown to be proportional to S log N. However, in many reallife imaging applications, the original Ssparse image may be blurred by an unknown point spread function defined over a domain Ω; this multiplies the apparent sparsity of the image, as well as the corresponding acquisition cost, by a factor of Ω. In this paper, we propose a new CS recovery algorithm for such images that can be modeled as a sparse superposition of pulses. Our method can be used to infer both the shape of the twodimensional pulse and the locations and amplitudes of the pulses. Our main theoretical result shows that our reconstruction method requires merely M = O(S + Ω) linear measurements, so that M is sublinear in the overall image sparsity SΩ. Experiments with real world data demonstrate that our method provides considerable gains over standard stateoftheart compressive sensing techniques in terms of numbers of measurements required for stable recovery. Index Terms — Compressive sensing, blind deconvolution, sparse approximation
A New Algorithm for the Automatic Search of the Best Delay in Blind Equalization
"... This paper deals with the problem of recovering the input signal applied to a linear timeinvariant system from the measures of its output and the apriori knowledge of the input statistics (blind equalization). Under the assumption of an i.i.d. nongaussian input sequence, a new iterative procedure ..."
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This paper deals with the problem of recovering the input signal applied to a linear timeinvariant system from the measures of its output and the apriori knowledge of the input statistics (blind equalization). Under the assumption of an i.i.d. nongaussian input sequence, a new iterative procedure based on phase sensitive highorder cumulants for adjusting the coefficients of a transversal equalizer is introduced. The main feature of the proposed technique is that it realizes the automatic selection of the equalization delay so as to improve the equalization performance. 1. INTRODUCTION Blind equalization [1] tries to recover the input to an unknown system from the measure of its output and the apriori knowledge of the statistics of its input. In the digital communication context, the input is the sequence of transmitted signals, while the system represents the linear distortion caused by the transmission channel between the source and the receiver. Blind equalization is useful to s...
Estimation of Image Corruption Inverse Function and Image Restoration using a PSObased Algorithm
"... A new method is proposed to estimate corruption function inverse of a blurred image. This technique can be used for restoring similar corrupted images. For linear position invariant procedure, the corruption process is modeled in the spatial domain by convolving the image with a point spread functio ..."
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A new method is proposed to estimate corruption function inverse of a blurred image. This technique can be used for restoring similar corrupted images. For linear position invariant procedure, the corruption process is modeled in the spatial domain by convolving the image with a point spread function (PSF) and addition of some noises into the image. It is assumed that a given artificial image is corrupted by a degradation function, represented by the PSF, and an additive noise. Then a filter mask (as a candidate for the corruption function inverse) is calculated to restore the original image from the corrupted one, with some accuracy. Calculating a suitable filter mask is formulated as an optimization problem: find optimal coefficients of the filter mask such that the difference between the original image and filter mask restored image to be minimized. Particle swarm optimization (PSO) is used to compute the optimal coefficients of the filter mask. Square filter masks are considered. A comparison between different exciting methods and the proposed technique is done using simulations. The simulation results show that the proposed method is effective and efficient. Since the proposed method is a simple linear technique, it can be easily implemented in hardware or software.
doi: 10.1049/ietspr.2008.0141
, 2008
"... Gradientadaptive algorithms for minimumphaseallpass decomposition of a finite impulse response system ..."
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Gradientadaptive algorithms for minimumphaseallpass decomposition of a finite impulse response system