Jérôme Gauthier's homepage

An important issue with oversampled FIR analysis filter banks (FBs) is to guarantee their FIR invertibility and to determine inverse synthesis FBs. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an inverse FIR synthesis system. We also provide a method to ensure the Hermitian symmetry property on the synthesis side, which is useful for processing real-valued signals. As an invertible analysis scheme corresponds to a redundant decomposition, there is no unique inverse FB. Given a particular solution, we parametrize the whole family of inverses through a null space projection. The resulting reduced parameter set allows us to simplify subsequent design procedures, since the perfect reconstruction constrained optimization problem is recast as an unconstrained optimization problem. The design of optimized FBs based on time or frequency localization criteria is then investigated, using a simple yet efficient gradient algorithm.

@Article{Gauthier_J_2008_sub_inv_oocfb,
  author = {Gauthier, J. and Duval, L. and Pesquet, J.-C.},
  title = {Optimization of Synthesis Oversampled Complex Filter Banks},
  booktitle = {Submitted},
  year = {2008},
}

Oversampled transforms are useful tools for data analysis, since redundancy increases freedom in the choice of the processing. We propose here a framework for oversampled lapped transform of images. More specifically, we establish conditions for perfect reconstruction of 2D data using non-separable windows. We also provide an example of a transform which relies on this approach. We also show the benefit of this technique in directional filtering applications encountered in the field of seismic data processing.

@INPROCEEDINGS{Gauthier_J_2005_peusipco_non_s2dcmltasdf,
  author = {Gauthier, J. and Duval, L. and Pesquet, J. C.},
  title = {A non separable {2D} complex modulated lapped transform 
           and its applications to seismic data filtering},
  booktitle = peusipco,
  year = {2005},
  month = {Sep.},
  location = {Antalya, Turkey},
}

In a previous work, we proposed a relatively simple method to build non separable perfect reconstruction oversampled lapped transforms. The main drawback of this method was that the redundancy factor was constrained to be equal to the overlapping one. This constitutes a strong limitation for applications such as seismic processing involving three-dimensional data sets. The memory requirements may indeed become hard to meet if the redundancy is not reduced. In this paper, we propose an approach to guarantee that a given lapped transform is invertible by a finite length filter bank. We show how to compute a corresponding synthesis filter bank. The proposed analysis/synthesis filter bank system is applied to directional filtering of noisy three-dimensional seismic data.

@INPROCEEDINGS{Gauthier_J_2006_picassp_low_rolta3Dsdf,
  author = {Gauthier, J. and Duval, L. and Pesquet, J. C.},
  title = {Low redundancy oversampled lapped transforms 
           and application to {3D} seismic data filtering},
  booktitle = picassp,
  year = {2006},
  volume = {2},
  pages = {821--824},
  location = {Toulouse, France},
  month = {May},
}

When an oversampled FIR filter bank structure is used for signal analysis, a main problem is to guarantee its invertibility and to be able to determine an inverse synthesis filter bank. As the analysis scheme corresponds to a redundant decomposition, there is no unique inverse filter bank and some of the solutions can lead to artifacts in textured image filtering applications. In this paper, the flexibility in the choice of the inverse filter bank is exploited to find the best-localized impulse responses. The design is performed by solving a constrained optimization problem which is reformulated in a smaller dimensional space. Application to seismic data clearly shows the improvements brought by the optimization process.

@INPROCEEDINGS{Gauthier_J_2007_picassp_ove_iclto,
  author = {Gauthier, J. and Duval, L. and Pesquet, J. C.},
  title = {Oversampled inverse complex lapped transform optimization},
  booktitle = picassp,
  year = {2007},
  volume = {1},
  pages = {549--552},
  month = {Apr.},
  location = {Honolulu, USA},
}

To help geologists in interpreting seismic data, we proposed in a previous article to perform directional filtering using oversampled complex lapped transforms. This 2D transform is extended in this paper to L dimensions, thus allowing to process 3D seismic data. We also propose a method to evaluate the relative importance of different orientations in seismic data. This evaluation is used to reduce potential errors in directional filtering, by adapting the processing to the ordered/disordered nature of data. Visual comparison between the former and the proposed methods are provided and show that chaotic areas are better preserved, while in ordered areas noise is accurately removed.

@INPROCEEDINGS{Gauthier_J_2007_psip_sei_dpcnsmlt,
  author = {Gauthier, J. and Duval, L.},
  title = {{3D} seismic data processing with complex non separable 
           multidimensional lapped transforms},
  booktitle = {Physics, sig. and image proc.},
  year = {2007},
  month = {Jan.},
  location = {Mulhouse, France},
}

Seismic data are subject to different kinds of unwanted perturbations. These random or organised noises, which can be acquisition or processing related for instance, may disturb geophysical interpretations and thwart attempts at automated processing methods. Since the relative features (e.g. amplitude, spectrum) of the signals of interest and the noises may vary locally, signal and noise separation is obtained by a local data-driven filtering with two or three-dimensional oversampled complex filter banks. Filter banks in general decompose the noisy data onto frequency bands and directions on restricted sub-regions (sub-images or sub-volumes), acting like a local FK with improved properties. The transforms studied in this work present sub-regions smooth overlapping, to avoid tiling effects while allowing signal reconstruction from the transformed domain. The proposed methodology uses limited redundancy filtering that both yield enhanced noise robustness (due to oversampling) and tractable 2D or 3D processing, since they are optimized to limit the redundancy cost. Coupling those redundant transforms with a processing method designed to detect and compute locally dominant directions, and to remove unwanted directions and random noise, leads to good visual results. Tests were performed on 2D and 3D seismic data.

@INPROCEEDINGS{Gauthier_J_2007_eage_loc_dusnfofb,
  author = {Gauthier, J. and Cacas, M.-C. and Duval, L.},
  title = {Local directional and uncoherent seismic noise filtering 
           with oversampled filter banks},
  booktitle = peage,
  year = {2007},
  month = {Jun.},
  location = {London},
}

The Short Term Fourier Transform (STFT) is a classical linear time-frequency (T-F) representation. Despites its relative simplicity, it has become a standard tool for the analysis of non-stationary signals. Since it provides a redundant representation, it raises some issues such as (i) "optimal" window choice for analysis, (ii) existence and determination of an inverse transformation, (iii) performance of analysis-modification-synthesis, or reconstruction of selected components of the time-frequency plane and (iv) redundancy controllability for low-cost applications, e.g. real-time computations. We address some of these issues, as well as the less often mentioned problem of transform symmetry in the inverse, through oversampled FBs and their optimized inverse(s) in a slightly more general setting than the discrete windowed Fourier transform.

@INPROCEEDINGS{Gauthier_J_2007_pspiewav_sho_tsasioifb,
  author = {Gauthier, J. and Duval, L. and Pesquet, J.-C.},
  title = {Short-term spectral Analysis and synthesis improvements with oversampled
	inverse filter banks},
  booktitle = pspiewav,
  year = {2007},
  month = {Aug.},
  location = {San Diego, USA},
}

Redundant filter bank inversion being an under-determined problem, we propose to use an optimization method to design a synthesis filter bank with good frequency responses. The constrained optimization problem is reformulated, using a Singular Value Decomposition, as an unconstrained minimization problem in a vector space of smaller dimension, thus significantly reducing computational complexity. These optimized low redundancy filter banks clearly lead to an improved performance in directional filtering applications.

@INPROCEEDINGS{Gauthier_J_2007_gretsi_con_bffr,
  author = {Gauthier, J. and Duval, L. and Pesquet, J. C.},
  title = {Construction de bancs de filtres faiblement redondants},
  booktitle = gretsi,
  year = {2007},
  pages = {965--968},
  month = {Sep.},
  location = {Troyes, France},
}

Redundancy in wavelets and filter banks has the potential to greatly improve signal and image denoising. Having developed a framework for optimized oversampled complex lapped transforms, we propose their association with the statistically efficient Stein's principle in the context of mean square error estimation. Under Gaussian noise assumptions, expectations involving the (unknown) original data are expressed using the observation only. Two forms of Stein's Unbiased Risk Estimators, derived in the coefficient and the spatial domain respectively, are proposed, the latter being more computationally expensive. These estimators are then employed for denoising with linear combinations of elementary threshold functions. Their performances are compared to the oracle, and addressed with respect to the redundancy. They are finally tested against other denoising algorithms. They prove competitive, yielding especially good results for texture preservation.

@INPROCEEDINGS{Gauthier_J_2008_peusipco_two_dsureletmcosd,
  author = {Gauthier, J. and Duval, L. and Pesquet, J. C.},
  title = {Two denoising Sure-let methods for complex
           oversampled subband decompositions},
  booktitle = peusipco,
  year = {2008},
}

The statistical model used to model the correlation noise at the turbo decoder for distributed video coding is studied in this paper. After working with several video sequences, we have shown that the classical model, based on Laplacian distribution, is not always producing accurate results. We propose to replace this model by a more general one, namely the Generalized Gaussian model. Two methods are then used to estimate the parameters of this model: the moment method and the maximum likelihood method. Tests are carried on in different settings: in on-line or off-line mode and with CIF or QCIF video, demonstrating that the Generalized Gaussian model seems more efficient than the Laplacian one.

@INPROCEEDINGS{Gauthier_J_2009_gretsi_ame_msbcvd,
  author = {Gauthier, J. and Maugey, T. and Pesquet-Popescu, B.},
  title = {Am\'elioration du mod\`ele statistique de bruit
pour le codage vid\'eo distribu\'e},
  booktitle = pgretsi,
  year = {2009},
  month = {Sep.},
  location = {Dijon, France}
}

@INPROCEEDINGS{Gauthier_J_2006_lmcs_inv_bfmbs,
  author = {Gauthier, J. and Duval, L.},
  title = {Inversion de bancs de filtres M bandes sur-\'echantillon\'es},
  booktitle = {LMCS},
  year = {2006},
  month = {Nov.},
  location = {Paris, France},
}

@MISC{Gauthier_J_2006_pat_met_isis,
  author = {Gauthier, J. and Duval, L. and Cacas, M.C.},
  title = {M\'ethode d'interpr\'etation stratigraphique d'images sismiques},
  year = {2006},
  note = {Brevet fran\c{c}ais, num\'ero nat. d'enregistrement : 06/10 493},
}

@PHDTHESIS{Gauthier_J_2008_phd,
  author = {Gauthier, J.},15:38 13/10/2008
  title = {Analyse de signaux et d'images par bancs de filtres. {A}pplications
	aux g\'eosciences.},
  school = {Universit\'e Paris-Est},
  year = {2008},
  month = {Jun.},
}