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14
Equivariant Adaptive Source Separation
 IEEE Trans. on Signal Processing
, 1996
"... Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Eq ..."
Abstract

Cited by 381 (10 self)
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Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Equivariant Adaptive Separation via Independence) . The EASI algorithms are based on the idea of serial updating: this specific form of matrix updates systematically yields algorithms with a simple, parallelizable structure, for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions and interference rejection levels depend only on the (normalized) distributions of the source signals. Close form expressions of these quantities are given via an asymptotic performance analysis. This is completed by some numerical experiments illustrating the effectiveness of the proposed ap...
Automated Segmentation of Multiple Sclerosis Lesions by . . .
, 2000
"... Quantitative analysis of MR images is becoming increasingly important in clinical trials in multiple sclerosis (MS). This paper describes a fully automated atlasbased technique for segmenting MS lesions from large data sets of multichannel MR images. The method simultaneously estimates the paramet ..."
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Cited by 49 (6 self)
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Quantitative analysis of MR images is becoming increasingly important in clinical trials in multiple sclerosis (MS). This paper describes a fully automated atlasbased technique for segmenting MS lesions from large data sets of multichannel MR images. The method simultaneously estimates the parameters of a stochastic model for normal brain MR images, and detects MS lesions as voxels that are not well explained by the model. It corrects for MR field inhomogeneities, estimates tissuespecific intensity models from the data itself, and incorporates contextual information in the MS lesion segmentation using a Markov random field. The results of the automated method were compared with lesions delineated by human experts, showing a high total lesion load correlation. When the degree of spatial correspondence between segmentations was taken into account, considerable disagreement was revealed, both between the expert manual segmentations, and between expert and automatic measurements.
RealTime Tracking of Highly Articulated Structures in the Presence of Noisy Measurements
, 2001
"... This paper presents a novel approach for modelbased realtime tracking of highly articulated structures such as humans. This approach is based on an algorithm which efficiently propagates statistics of probability distributions through a kinematic chain to obtain maximum a posteriori estimates of th ..."
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Cited by 39 (2 self)
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This paper presents a novel approach for modelbased realtime tracking of highly articulated structures such as humans. This approach is based on an algorithm which efficiently propagates statistics of probability distributions through a kinematic chain to obtain maximum a posteriori estimates of the motion of the entire structure. This algorithm yields the least squares solution in linear time (in the number of components of the model) and can also be applied to nonGaussian statistics using a simple but powerful trick. The resulting implementation runs in realtime on standard hardware without any preprocessing of the video data and can thus operate on live video. Results from experiments performed using this system are presented and discussed.
Segmentation of Multiple Motions by Edge Tracking between Two Frames
 in British Machine Vision Conference
, 2000
"... This paper presents a method for segmenting multiple motions using edges. Recent work in this field has been constrained to the case of two motions, and this paper demonstrates that the approach can be extended to more than two motions. The image is first segmented into regions, and then the framewo ..."
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Cited by 5 (0 self)
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This paper presents a method for segmenting multiple motions using edges. Recent work in this field has been constrained to the case of two motions, and this paper demonstrates that the approach can be extended to more than two motions. The image is first segmented into regions, and then the framework determines the motions present and labels the edges in the image. Initialisation is particularly difficult, and a novel scheme is proposed which recursively splits motions to provide the ExpectationMaximisation algorithm with a reasonable guess, and a Minimum Description Length approach is used to determine the best number of models to use. The edge labels are then used to determine the the region labelling. A global optimisation is introduced to refine the motions and provide the most likely region labelling. 1
On the Coherence of Supremum Preserving Upper Previsions
 IN PROCEEDINGS OF IPMU '96 (SIXTH INTERNATIONAL CONFERENCE ON INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGEBASED SYSTEMS
, 1996
"... We study the relation between possibility measures and the theory of imprecise probabilities. It is shown that a possibility measure is a coherent upper probability iff it is normal. We also prove that a possibility measure is the restriction to events of the natural extension of a special kind of u ..."
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Cited by 5 (4 self)
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We study the relation between possibility measures and the theory of imprecise probabilities. It is shown that a possibility measure is a coherent upper probability iff it is normal. We also prove that a possibility measure is the restriction to events of the natural extension of a special kind of upper probability, defined on a class of nested sets. Next, we go from upper probabilities to upper previsions. We show that if a coherent upper prevision defined on the convex cone of all positive gambles is supremum preserving, then it must take the form of a Shilkret integral associated with a possibility measure. But at the same time, we show that a supremum preserving upper prevision is not necessarily coherent! This makes us look for alternative extensions of possibility measures that are not necessarily supremum preserving, through natural extension.
Don’t shed tears over breaks
 DMV Nachrichten
, 2005
"... imaging Mathematical Subject Classification: 93E14, 62G08, 68T45, 49M20, 90C31 This essay deals with ‘discontinuous phenomena ’ in timeseries. It is an introduction to, and a brief survey of aspects concerning the concepts of segmentation into ‘smooth ’ pieces on the one hand, and the complementary ..."
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Cited by 4 (4 self)
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imaging Mathematical Subject Classification: 93E14, 62G08, 68T45, 49M20, 90C31 This essay deals with ‘discontinuous phenomena ’ in timeseries. It is an introduction to, and a brief survey of aspects concerning the concepts of segmentation into ‘smooth ’ pieces on the one hand, and the complementary notion of the identification of jumps, on the other hand. We restrict ourselves to variational approaches, both in discrete, and in continuous time. They will define ‘filters’, with data as ‘inputs ’ and minimizers of functionals as ‘outputs’. The main example is a particularly simple model, which, for historical reasons, we decided to call the Potts functional. We will argue that it is an appropriate tool for the extraction of the simplest and most basic morphological features from data. This is an attempt to interpret data from a welldefined point of view. It is in contrast to restoration of a true signal perhaps distorted and degraded by noise which is not in the main focus of this paper.
Robust Locally Linear Analysis with Applications to Image Denoising and Blind Inpainting
, 2011
"... We study the related problems of denoising images corrupted by impulsive noise and blind inpainting (i.e., inpainting when the deteriorated region is unknown). Our basic approach is to model the set of patches of pixels in an image as a union of low dimensional subspaces, corrupted by sparse but pe ..."
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Cited by 4 (1 self)
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We study the related problems of denoising images corrupted by impulsive noise and blind inpainting (i.e., inpainting when the deteriorated region is unknown). Our basic approach is to model the set of patches of pixels in an image as a union of low dimensional subspaces, corrupted by sparse but perhaps large magnitude noise. For this purpose, we develop a robust and iterative RANSAC like method for single subspace modeling and extend it to an iterative algorithm for modeling multiple subspaces. We prove convergence for both algorithms and carefully compare our methods with other recent ideas for such robust modeling. We demonstrate state of the art performance of our method for both imaging problems.
Robust Boltzmann Machines for Recognition and Denoising
"... While Boltzmann Machines have been successful at unsupervised learning and density modeling of images and speech data, they can be very sensitive to noise in the data. In this paper, we introduce a novel model, the Robust Boltzmann Machine (RoBM), which allows Boltzmann Machines to be robust to corr ..."
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Cited by 3 (0 self)
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While Boltzmann Machines have been successful at unsupervised learning and density modeling of images and speech data, they can be very sensitive to noise in the data. In this paper, we introduce a novel model, the Robust Boltzmann Machine (RoBM), which allows Boltzmann Machines to be robust to corruptions. In the domain of visual recognition, the RoBM is able to accurately deal with occlusions and noise by using multiplicative gating to induce a scale mixture of Gaussians over pixels. Image denoising and inpainting correspond to posterior inference in the RoBM. Our model is trained in an unsupervised fashion with unlabeled noisy data and can learn the spatial structure of the occluders. Compared to standard algorithms, the RoBM is significantly better at recognition and denoising on several face databases. 1.
Complexity Penalized Sums of Squares for Time Series: Rigorous Analytical Results
, 2005
"... A simple variational approach to the estimation of timeseries is studied in detail and mathematical rigor. The functional in question is a complexity penalized sum of squares. The results include existence, uniqueness, continuous dependence on parameters, and stability, in dependence of parameters a ..."
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Cited by 1 (1 self)
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A simple variational approach to the estimation of timeseries is studied in detail and mathematical rigor. The functional in question is a complexity penalized sum of squares. The results include existence, uniqueness, continuous dependence on parameters, and stability, in dependence of parameters and data, of the statistical estimate.
ROBUST ADAPTIVE METROPOLIS ALGORITHM WITH COERCED ACCEPTANCE RATE
"... Abstract. The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223242] uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new robust adaptive Metropolis algorithm estimating the shape of the target dis ..."
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Cited by 1 (0 self)
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Abstract. The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223242] uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new robust adaptive Metropolis algorithm estimating the shape of the target distribution and simultaneously coercing the acceptance rate. The adaptation rule is computationally simple adding no extra cost compared with the AM algorithm. The adaptation strategy can be seen as a multidimensional extension of the previously proposed method adapting the scale of the proposal distribution in orderto attain agiven acceptancerate. The empiricalresults showpromising behaviour of the new algorithm in an example with Student target distribution having no finite second moment, where the AM covariance estimate is unstable. Furthermore, in the examples with finite second moments, the performance of the new approach seems to be competitive with the AM algorithm combined with scale adaptation. 1.