Showing papers by "Jean-Christophe Pesquet published in 2003"

A nonlinear diffusion-based three-band filter bank

Abstract: In this letter, we revisit a number of concepts that have recently proven to be useful in multiresolution signal analysis, specifically by replacing the now classical linear-scale transition operators by nonlinear ones. More precisely, we address the problem of designing appropriate operators associated to nonlinear filter banks using multiscale analysis. We first establish a connection between nonlinear filter banks and partial differential equations operators used in scale-space theory. Toward this end, we propose specific structures of nonlinear three-band decompositions ensuring a perfect reconstruction. The behavior of the proposed structures is analyzed for a step-like signal in a high SNR scenario, and a simulation is proposed for a more complex scenario.

Image deconvolution with total variation bounds

Abstract: Total variation has been used exclusively as an objective in the formulation of image deconvolution problems. In this paper, we propose an alternative framework in which total variation is used as a constraint. In contrast with the standard approach, this framework requires an a priori bound on the total variation of the original image, while no a priori information on the noise is necessary. Furthermore, it places no limitation on the incorporation of additional constraints in the recovery process and can be solved efficiently via powerful block-iterative methods.

Source separation of a class of non linear time series

Abstract: This paper deals with blind source separation of non linear signals. We therefore consider non i.i.d. source signals which are mixed by an unknown convolutive filter. Previous approaches succeeded in designing contrasts which are valid for non i.i.d. sources, but which cannot be handled easily in practice. Starting from this point, we propose some improvements and simplifications of the contrasts for the general class of non i.i.d. multiplicative-like signals: the obtained criteria are also expected to exhibit better statistical performances. Classical optimization algorithms are used for the local maximization of the contrasts, and genetic algorithms are tested in order to reach the global maximum of our criteria. Simulations prove the validity of our contrasts and illustrate the difficulty to choose the most appropriate one.

Vector-lifting schemes based on sorting techniques for lossless compression of multispectral images

Abstract: Vector-liftingschemesbasedonsortingtechniquesforlosslesscompressionofmultisp ectralimagesA. Benazza-BenyahiaaandJ. -C.PesquetbaDepartementdeMathematiquesAppliquees,Signal etCommunicationsEcoleSuperieuredesCommunications (SUP'COM),TunisiabIGM andURACNRS820,UniversitedeMarne-la-Vallee, FranceABSTRACTInthispap er,weintro ducevector-lifting schemeswhich allowtogenerate very compactmultiresolution rep-resentations,suitableforlosslessandprogressiveco dingofmultisp ectralimages.Thesenewdecomp ositionschemesexploitsimultaneouslythespatialandsp ectralredundanciescontainedinmultisp ectralimages.When the sp ectral bands have di erent dynamic ranges, weimproe dramatically the p erformances of the pro-posed schemes by a reversible histogram mo di cation based on sorting p ermutations.Simulation tests carriedout on real images allowto evaluate the p erformances of this new compression metho d.They indicate that theachieved compression ratios are higher than those obtained with currently used lossless co ders.Keywords:Multicomp onentimages,lossless andprogressive co ding,nonlinear subbanddecomp osition,his-togram mo di cation.1. INTRODUCTIONAmultisp ectral image results from the sensing of a terrestrial area at di erentwavelengths. These images providevaluable information concerning the land coer of the sensed region.This is the reason why they are frequentlyused in several applications such as agriculture, geography, geology....Furthermore, it is exp ected that largerand larger amounts of data will b e generated thanks to the continuous improvement and increased p opularityof remote sensing systems.In this context, an imp ortant issue in multisp ectral imaging is the large amountofdata to b e transmitted or stored.To give an idea of the imp ortance of the problem, we recall that it is estimatedthat the Earth Observation System Data and Information System generates more than one terabyte of data p erday.This amount of data requires huge storage capabilities.In order to solve this problem, image compressiontechniques are clearly required.In this pap er, we are interested in lossless co ding techniques for multisp ectralimagesb ecausetheleastdistortionoftheseisgenerallynottoleratedsinceitmayleadtoincorrectcomputation of physical ground parameters.Besides, progressive reconstruction is a very app ealing functionalityin the context of image telebrowsing.It consists in realizing a multiresolution co ding of the image:the rst levelof resolution corresp onds to a very compressed version of the original image and the successive ones provide moredetails until the image is completely recovered.For this purp ose, lifting-schemes1{3hae b een found to b e verypowerful to ols since they provide very compact multiresolution representations of the input images.4For thisreason, they have b een retained in the standard JPEG 2000.5In recentworks,6, 7wehaeintro duced vector-lifting decomp ositions suitable for co ding multisp ectral images since they exploit simultaneously the sp ectral andthe spatial redundancies.When the sp ectral bands havevery di erent dynamic ranges, the sp ectral decorrelationmaybelimited.In thispap er,we prop ose to improve dramatically the p erformances of theseapproaches byapplying a reversible histogram mo di cation based on sorting p ermutations.This pap er is organized as follows.Further author information:(Send corresp ondence to A. Benazza-Benyahia),A.Benazza-Benyahia,EcoleSuperieuredesCommunications(SUP'COM),CiteTechnologiqueunications,Route de Raoued Km 3.5, 2083 El Ghazala, Ariana, Tunisia, E-mail:b en.yahia@planet.tn, Telephone:+216 71 85 7000, Fax:+216 71 85 68 29,J. -C. Pesquet, IGM and URA CNRS 820, Universite de Marne-la-Vallee, 5, Bd Descartes, Champs sur Marne, 77454Marne la Vallee Cedex 2, France, E-mail:p esquet@univ-mlv.fr, Telephone:+3316095 7739 Fax:+ 33 1 60 95 72 14

Total variation information in image recovery

Abstract: Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective to be minimized under a single constraint. In this paper, we propose an alternative framework in which total variation is used as a constraint in a general quadratic programming context. The advantage of this approach is that it allows for a wider range of constraints to be easily incorporated in the recovery process.

Adapted vector-lifting schemes for multiband textured image coding

Abstract: In this paper, we address the problem of coding textured and multiband images for storage applications. More precisely, attention is paid to telebrowsing applications which require progressive reconstruction. The contribution of the paper is the design of a generalized vector-lifting scheme for building multiresolution representations adapted to the spatial, spectral and frequential content of the images. Simulations performed on real data indicate that a reduced data rate is obtained with the proposed method.

Séparation aveugle d'un mélange convolutif de sources non linéaires par une approche hiérarchique

Abstract: This paper deals with blind source separation of convolutive mixtures of non linear (and hence non i.i.d.) sources. This general framework, although rarely treated in literature, is of great importance in applications. An iterative method was proposed [10]; however, the deflation procedure induces an error accumulation effect. We propose a hierarchical approach inspired from [6] which is less sensitive to error accumulation. We prove the validity of the method and its convergence to a separating filter in the general case of non linear sources. Finally, simulations confirm our theoretical considerations for classical non linear processes (ARCH).