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| Catch a Wavelet 2004 |
28 Jun 2004 at 11:15, Room BM5.202
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| Nonlinear signal processing techniques for direction-of-arrival estimation
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| G.V. Anand, Indian Institute of Science, Bangalore
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Several high- resolution direction-of-arrival (DOA) estimation techniques such as MUSIC are currently in use. The performance of these techniques is known to degrade as the signal-to-noise ratio (SNR) is decreased, and the degradation becomes unacceptably large for SNR typicaly below 0 dB. This degradation in performance may be arrested by the application of appropriate preprocessing techniques to boost the SNR prior to DOA estimation. In this talk, two SNR enhancement techniques will be presented, viz.(1) wavelet array denoising under Gaussian noise, and (2) stochastic resonance under non-Gaussian noise. Simulation results will be presented to illustrate the improvement in the DOA estimation performance of MUSIC due to the application of these preprocessing techniques.
About the author
G.V.Anand is a professor of the Department of Electrical Communication Engineering in Indian Institute of Science, Bangalore. He has received his B.Sc (1962) and M.Sc (1964) from Osmania University, Hyderabad, India. He got his Ph.D (1969) from the Indian Institute of Science, Bangalore. He then joined the faculty of IISc as lecturer, ECE Department, in 1969. Dr. Anand is a professor since 1984.
Commonwealth Academic Staff Fellow, University College, London (1978-79)
Visiting Scientist, Naval Physical & Oceanographic Laboratory, Cochin,India (1996-97)
Invited Professor, University of Angers, France (2002 and 2004)
Visiting Professor, Cankaya University, Ankara, Turkey (2003-04)
Fellow of Indian Academy of Sciences, Indian National Academy of Engineering, Institution of Electronics and Telecommunication Engineers of India, Acoustical Society of India.
Research interests : mathematical modeling of undersea sound propagation, inverse problems in ocean acoustics, statistical signal processing, nonlinear dynamics. |
24 Jun 2004 at 17:15, Room CO-015
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| Hybrid waveform audio models
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| Dr. Bruno Torresani, Université de Provence, Marseille, France
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Audiophonic signals have the peculiarity of involving significantly different components (transients, tonals,...). We describe the main features of a novel approach for modeling and coding such signals. The approach combines non-linear transform coding and structured approximation techniques (using simultaneously local cosine and wavelet bases), together with hybrid modeling of the signal class under consideration. In a few words, several different components of the signal are estimated and transform coded using an appropriately chosen orthonormal basis. We will discuss different random signal models and corresponding estimation procedures, and provide numerical results and audio illustrations. This talk is based on joint works with Laurent Daudet and Stéphane Molla, and previous collaborations with P. Guillemain and R. Kronland-Martinet.
About the author
B. Torrésani graduated from Université de Provence, Marseille in 1986, and got his habilitation degree from "Université de la Méditerranée", Marseille, in 1992. He has been "Chargé de Recherches" at CNRS from 1989 to 1998, and is currently professor at Université de Provence, in both Physics and Mathematics departments. His research interests include mathematical methods for signal processing (with emphasis on audio signal modeling), time-frequency and wavelet methods, and computational genetics. Among other publications, he authored the books "Noncommutative Distributions" (Marcel Dekker, 1993, with S. Albeverio, R. Hoegh-Krohn, J. Marion and D. Testard), "Analyse continue par ondelettes" (InterEditions, 1995) and "Practical Time-Frequency Analysis" (Academic Press, 1997, with R. Carmona and W.L. Hwang). |
10 Jun 2004 at 17:15, Room CO-015
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| Some aspects of Huang's Empirical Mode Decomposition, from interpretation to applications
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| Dr. Patrick Flandrin, Ecole Normale Supérieure de Lyon, France
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Empirical Mode Decomposition (EMD) has recently been pioneered by N.E. Huang et al. as a local and fully data-driven technique aimed at decomposing nonstationary multicomponent signals in "intrinsic" AM-FM contributions. Although the EMD principle is appealing and its implementation easy, performance analysis is difficult since no analytical description of the method is available. We will here report on numerical simulations illustrating the potentialities and limitations of EMD in a number of specific situations. First, we will show that, when applied to the versatile, broadband, model of fractional Gaussian noise (fGn), the experimental spectral analysis of the obtained modes reveal an equivalent filter bank structure which shares most properties of a wavelet decomposition in the same context, in terms of self-similarity, quasi-decorrelation and variance progression. Second, EMD-based approaches to denoising and detrending signal+noise mixtures will be considered from partial reconstructions, the relevant modes being selected on the basis of the statistical properties of modes that have been empirically established.
(Joint work with Paulo Gonçalvès and Gabriel Rilling.)
About the author
Patrick Flandrin holds a "Thèse d'Etat ès Sciences Physiques" from Institut National Polytechnique de Grenoble (1987). He is currently "Directeur de Recherche" at CNRS, within the Physics Department of Ecole Normale Supérieure de Lyon, France. His research interests include mainly nonstationary signal processing (with emphasis on time-frequency and time-scale methods) and the study of self-similar stochastic processes. Among many other publications in theses areas, Patrick Flandrin authored the book "Temps-Fréquence" (Paris: Hermes, 1993 and 1998), translated into English as "Time-Frequency/Time-Scale Analysis" (San Diego: Academic Press, 1999). He is a Fellow of the IEEE and he has been awarded the Philip Morris Scientific Prize in Mathematics in 1991, the SPIE Wavelet Pioneer Award in 2001 and the Prix Michel Monpetit from the French Academy of Sciences in 2001. |
27 May 2004 at 16:15, Room CO-015
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| How to Exploit Directional Features in Images
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| Vladan Velisavljevic, LCAV
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The standard 2-D wavelet transform is widely used in image processing with a great success. It is a separable transform allowing for a simple filter design and low computational complexity. However, it fails to capture efficiently phenomena in images in directions other than the horizontal and vertical.
Recently, many approaches have been made to exploit geometrical features in images. These include curvelets, contourlets, wedgelets, directional filter banks, etc. Although they provide sparser representations in the transform domain, they are computationally complex or involve complicated filter design.
Our goal is to retain computational simplicity of the standard wavelet transform and to make use of directional coherences in images. We propose multi-directional wavelet transform that is capable of providing efficient representation of images. The proposed transform can be easily applied in all areas of image processing where the standard 2-D wavelet transform is used. In particular, some promising results have been obtained in compression and denoising of images. |
13 May 2004 at 16:15, Room CM-106
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| Regularized image reconstruction in multiresolution spaces from non-uniform samples
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| Muthuvel Arigovindan, Biomedical Imaging Group, EPFL
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We propose a novel method for image reconstruction from non-uniform samples with no constraints on their locations. We adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms:
(i) the sum of squared errors at the specified points;
(ii) a quadratic functional that penalizes the lack of smoothness.
We search for a solution that is a uniform spline and show how it can be determined by solving a large, sparse system of linear equations. Using the two-scale relation for B-splines, we derive an algebraic relation that links together the linear systems of equations specifying reconstructions at different levels of resolution. We use this relation to develop a fast wavelet-like multiresolution algorithm. We demonstrate the effectiveness of our approach on some image reconstruction examples. |
22 Apr 2004 at 17:15, Room CO-015
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| Resolution enhancement and sampling with wavelets and footprints
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| Dr. Pier Luigi Dragotti, Communications and Signal Processing Group, Imperial College, London, UK
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In this talk, we consider classes of non-bandlimited signals, namely, 1-D streams of Diracs and 1-D piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution structure of the wavelet transform, these new sampling theorems naturally lead to the development of a new resolution enhancement algorithm based on
wavelet footprints. Preliminary results show the potentiality of this algorithm. Extensions to multi-dimensional signals are also highlighted.
This is joint work with Martin Vetterli (EPFL) and Pancham Shukla (Imperial College). |
15 Apr 2004 at 17:15, Room CM-201
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| A mathematical comparison of different concepts for image denoising
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| Prof. Dr. Peter Maass, University Of Bremen, Germany
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Multiscale denoising, which also allows to emphasis certain image structures, has become the standard technique for enhancing image quality. The most prominent examples of tese techniques include wavelet shrinkage methods and non-linear diffusion equations. We will investigate the mathematical analogies between these different concepts, in particular we will derive a partical differntial equation, whose solution is equivalent to wavelet shrinkage. An application of wavelet shrinkage to medical imaging (EEG prenatal diagnosis) illustrates the potential for denoising as well as for strucutre-separation of this method.
About the author
Prof. Dr. Peter Maass is the Director of Center of Industrial Mathematics at the University of Bremen and the Vice-President of the German Math. Society. |
08 Apr 2004 at 17:15, Room CO-015
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| Do Wavelets Really Provide Correct Answers in Two Dimensions?
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| Rahul Shukla, LCAV
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We begin with considering a simple example of piecewise linear image, which shows the inherent weakness of separable construction of wavelets in two dimensions (2-D). This weakness essentially limits the performance of wavelets for image processing problems such as approximation and compression. To have a clear picture, we return to the one dimensional (1-D) case and study the problem of compression of piecewise polynomial signals. Again we observe the sub-optimal R-D performance by the wavelet based schemes in 1-D, where wavelets are supposed to perform well. The reason is its failure to efficiently code singularities of signals. And this problem becomes even greater in 2-D, where curvilinear singularities, like edges, represent one of the most important perceptual and objective information in an image.
As wavelet based schemes fail to explore the geometrical structure that is typical in smooth edges of images, we need new schemes capable of exploiting the geometrical information present in images. Since both the computational efficiency and precise modeling of geometrical information are key issues in the compression problem, we present novel coding algorithms based on tree structured segmentation.We first investigate both the one dimensional (1-D) and two dimensional (2-D) piecewise polynomials signals. For the 1-D case, our scheme is based on binary tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly and is called prune-join algorithm. This allows to achieve the correct exponentially decaying R-D behavior, D(R)~2^{-cR} , thus improving over classical wavelet schemes. We then show the extension of this scheme to the 2-D case using a quadtree, which also achieves the exponentially decaying R-D behavior, for the polygonal model, with low computational cost of O(NlogN). Again, the key is an R-D optimized prune and join strategy.
We further present the R-D performance of the proposed tree algorithms for piecewise smooth signals. We show that the proposed algorithms achieve the near-optimal polynomially decaying asymptotic R-D behavior for both the 1-D and 2-D scenarios. Finally, we conclude with numerical results, which show that the proposed quadtree coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp. |
25 Mar 2004 at 17:15, Room CO-015
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| Image Processing by The Curvelet Transform
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| Dr Jean-Luc Starck, CEA, Centre de Saclay, France
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Wavelets have been very successful for many applications such as filtering, deconvolution, detection or compression. They have however some limitations when the data present anisotropic features, and we present new methods, such as the ridgelets and the curvelets, better adapted to this kind of data. Finally, we describe how to combine all these transforms in order to benefit of the advantages of each of them.
About the author
Jean-Luc Starck holds a Ph.D from University Nice-Sophia Antipolis and an Habilitation from University Paris XI. He was a visitor at the European Southern Observatory (ESO) in 1993 and at Stanford's statistics department in 2000. He has been a Researcher at CEA since 1994. His research interests include image processing, multiscale methods and statistical methods in astrophysics. He is also author of two books entitled Image Processing and Data Analysis: the Multiscale Approach (Cambridge University Press, 1998), and Astronomical Image and Data Analysis (Springer, 2002). |
11 Mar 2004 at 17:15, Room CO-015
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| Autofocusing in digital holography via sparse image representations
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| Michael Liebling, Biomedical Imaging Group, EPFL
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| The numerical reconstruction of digital Fresnel holograms involves the simulation of a propagating complex wave. Finding the appropriate propagation distance, where the wavefront is ``in-focus'', is difficult if done manually and calls for an automatic procedure. We give a brief review of previously proposed autofocusing methods and propose an algorithm to overcome some of their limitations, in particular, their sensitivity to noise. We propose a method maximizing an image sharpness metric related to the sparsity of the signal's expansion in distance-dependent waveletlike bases (Fresnelets). We show the benefits of such an approach over others and present results based on simulations and experimental measurements. |
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