@ARTICLE{Gauthier_J_2009_j-ieee-tsp_optimization_socfb,
  author = {Gauthier, J. and Duval, L. and Pesquet, J.-C.},
  title = {Optimization of Synthesis Oversampled Complex Filter Banks},
  journal = j-ieee-tsp,
  year = {2009},
  volume = {57},
  pages = {3827--3843},
  number = {10},
  month = {Oct.},
  keywords = {Data mining Discrete Fourier transforms Finite impulse response filter
	IEEE Optimization Oversampled filter banks Polynomials Probability
	density function filter design frequency localization inversion lapped
	transforms modulated filter banks optimization time localization},
  file = {Gauthier_J_2009_j-ieee-tsp_optimization_socfbb.pdf:Gauthier_J_2009_j-ieee-tsp_optimization_socfbb.pdf:PDF;Gauthier_J_2009_j-ieee-tsp_optimization_socfb-published.pdf:Gauthier_J_2009_j-ieee-tsp_optimization_socfb-published.pdf:PDF},
  abstract = {An important issue with oversampled FIR analysis filter banks (FBs)
	is to determine inverse synthesis FBs, when they exist. 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 serviceable to 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 parameterize the whole family of inverses through a
	null space projection. The resulting reduced parameter set simplifies
	design procedures, since the perfect reconstruction constrained optimization
	problem is recast as an unconstrained optimization problem. The design
	of optimized synthesis FBs based on time or frequency localization
	criteria is then investigated, using a simple yet efficient gradient
	algorithm.},
  doi = {10.1109/TSP.2009.2023947},
  issn = {1053-587X},
  owner = {duvall},
  pdf = {Gauthier_J_2009_tsp_opt_socfb-published.pdf},
  timestamp = {2009.06.11}
}



@ARTICLE{Chaux_C_2008_j-ieee-tsp_nonlinear_sbemid,
  author = {Chaux, C. and Duval, L. and Benazza-Benyahia, A. and Pesquet, J.-C.},
  title = {A nonlinear {Stein} based estimator for multichannel image denoising},
  journal = j-ieee-tsp,
  year = {2008},
  volume = {56},
  pages = {3855--3870},
  number = {8},
  month = {Aug.},
  file = {Chaux_C_2008_j-ieee-tsp_nonlinear_sbemid.pdf:Chaux_C_2008_j-ieee-tsp_nonlinear_sbemid.pdf:PDF},
  abstract = {The use of multicomponent images has become widespread with the improvement
	of multisensor systems having increased spatial and spectral resolutions.
	However, the observed images are often corrupted by an additive Gaussian
	noise. In this paper, we are interested in multichannel image denoising
	based on a multiscale representation of the images. A multivariate
	statistical approach is adopted to take into account both the spatial
	and the inter-component correlations existing between the different
	wavelet subbands. More precisely, we propose a new parametric nonlinear
	estimator which generalizes many reported denoising methods. The
	derivation of the optimal parameters is achieved by applying Stein's
	principle in the multivariate case. Experiments performed on multispectral
	remote sensing images clearly indicate that our method outperforms
	conventional wavelet denoising techniques},
  doi = {10.1109/TSP.2008.921757},
  issn = {1053-587X},
  owner = {duvall},
  timestamp = {2006.10.26}
}
@ARTICLE{Chaux_C_2006_j-ieee-tip_image_adtmbwt,
  author = {Chaux, C. and Duval, L. and Pesquet, J.-C.},
  title = {Image analysis using a dual-tree ${M}$-band wavelet transform},
  journal = j-ieee-tip,
  year = {2006},
  volume = {15},
  pages = {2397--2412},
  number = {8},
  month = {Aug.},
  keywords = {Hilbert wavelet pair;denoising comparisons;directional analysis;dual
	basis;dual-tree M-band wavelet transform;dual-tree decomposition
	structure;estimation errors;image analysis;optimal signal reconstruction
	technique;thresholding strategies;two-dimensional generalization;Hilbert
	transforms;image denoising;image reconstruction;image representation;trees
	(mathematics);wavelet transforms;Algorithms;Artificial Intelligence;Image
	Enhancement;Image Interpretation, Computer-Assisted;Information Storage
	and Retrieval;Numerical Analysis, Computer-Assisted;Pattern Recognition,
	Automated;Signal Processing, Computer-Assisted;},
  file = {Chaux_C_2006_j-ieee-tip_image_adtmbwt.pdf:Chaux_C_2006_j-ieee-tip_image_adtmbwt.pdf:PDF},
  abstract = {We propose a two-dimensional generalization to the M-band case of
	the dual-tree decomposition structure (initially proposed by Kingsbury
	and further investigated by Selesnick) based on a Hilbert pair of
	wavelets. We particularly address: 1) the construction of the dual
	basis and 2) the resulting directional analysis. We also revisit
	the necessary pre-processing stage in the M-band case. While several
	reconstructions are possible because of the redundancy of the representation,
	we propose a new optimal signal reconstruction technique, which minimizes
	potential estimation errors. The effectiveness of the proposed M-band
	decomposition is demonstrated via denoising comparisons on several
	image types (natural, texture, seismics), with various M-band wavelets
	and thresholding strategies. Significant improvements in terms of
	both overall noise reduction and direction preservation are observed.},
  doi = {10.1109/TIP.2006.875178},
  issn = {1057-7149},
  owner = {duvall},
  timestamp = {2006.04.27}
}
@ARTICLE{Chaux_C_2007_j-ieee-tit_noise_cpdtwd,
  author = {Chaux, C. and Pesquet, J.-C. and Duval, L.},
  title = {Noise covariance properties in dual-tree wavelet decompositions},
  journal = j-ieee-tit,
  year = {2007},
  volume = {53},
  pages = {4680--4700},
  number = {12},
  month = {Dec.},
  file = {Chaux_C_2007_j-ieee-tit_noise_cpdtwd.pdf:Chaux_C_2007_j-ieee-tit_noise_cpdtwd.pdf:PDF},
  abstract = {Dual-tree wavelet decompositions have recently gained much popularity,
	mainly due to their ability to provide an accurate directional analysis
	of images combined with a reduced redundancy. When the decomposition
	of a random process is performed --- which occurs in particular when
	an additive noise is corrupting the signal to be analyzed --- it
	is useful to characterize the statistical properties of the dual-tree
	wavelet coefficients of this process. As dual-tree decompositions
	constitute overcomplete frame expansions, correlation structures
	are introduced among the coefficients, even when a white noise is
	analyzed. In this paper, we show that it is possible to provide an
	accurate description of the covariance properties of the dual-tree
	coefficients of a wide-sense-stationary process. The expressions
	of the (cross-) covariance sequences of the coefficients are derived
	in the one- and two-dimensional cases. Asymptotic results are also
	provided, allowing to predict the behavior of the second-order moments
	for large lag values or at coarse resolution. In addition, the cross-correlations
	between the primal and dual wavelets, which play a primary role in
	our theoretical analysis, are calculated for a number of classical
	wavelet families. Simulation results are finally provided to validate
	these results.},
  doi = {10.1109/TIT.2007.909104},
  owner = {duvall},
  timestamp = {2006.04.27}
}

@INCOLLECTION{Chaux_C_2009_incoll_wavelet_tdmi,
  author = {Chaux, C. and Benazza-Benyahia, A. and Pesquet, J.-C. and Duval,
	L.},
  title = {Wavelet Transform for the Denoising of Multivariate Images},
  year = {2009},
  pages = {203--238},
  crossref = {Chanussot_J_2009_book_mul_ip},
  file = {Chaux_C_2009_incoll_wavelet_tdmi.pdf:Chaux_C_2009_incoll_wavelet_tdmi.pdf:PDF},
  owner = {duvall},
  pdf = {Chaux_C_2009_inbook_wav_tdmi.pdf},
  timestamp = {2009.11.23}
}

@ARTICLE{Jacques_L_2011_j-sp_pan_mgrisdfs,
  author = {L. Jacques and L. Duval and C. Chaux and G. Peyr{\'e}},
  title = {A panorama on multiscale geometric representations, intertwining
	spatial, directional and frequency selectivity},
  journal = j-sp,
  year = {2011},
  volume = {91},
  pages = {2699--2730},
  number = {12},
  month = {Dec.},
  keywords = {previous termMultiscale; Geometric representationsnext term; Oriented
	decompositions; Scale-space; Wavelets; Atoms; Sparsity; Redundancy;
	Bases; Frames; Edges; Textures; Image processing; Haar wavelet; Non-Euclidean
	wavelets},
  file = {Jacques_L_2011_j-sp_pan_mgrisdfs.pdf:Jacques_L_2011_j-sp_pan_mgrisdfs.pdf:PDF;:Jacques_L_2011_j-sp_pan_mgrisdfs-elsevier.htm:URL;Jacques_L_2011_j-sp_pan_mgrisdfs-preprint.pdf:Jacques_L_2011_j-sp_pan_mgrisdfs-preprint.pdf:PDF;Jacques_L_2011_j-sp_pan_mgrisdfs-proof.pdf:Jacques_L_2011_j-sp_pan_mgrisdfs-proof.pdf:PDF},
  abstract = {The richness of natural images makes the quest for optimal representations
	in image processing and computer vision challenging. The latter observation
	has not prevented the design of image representations, which trade
	off between efficiency and complexity, while achieving accurate rendering
	of smooth regions as well as reproducing faithful contours and textures.
	The most recent ones, proposed in the past decade, share a hybrid
	heritage highlighting the multiscale and oriented nature of edges
	and patterns in images. This paper presents a panorama of the aforementioned
	literature on decompositions in multiscale, multi-orientation bases
	or dictionaries. They typically exhibit redundancy to improve sparsity
	in the transformed domain and sometimes its invariance with respect
	to simple geometric deformations (translation, rotation). Oriented
	multiscale dictionaries extend traditional wavelet processing and
	may offer rotation invariance. Highly redundant dictionaries require
	specific algorithms to simplify the search for an efficient (sparse)
	representation. We also discuss the extension of multiscale geometric
	decompositions to non-Euclidean domains such as the sphere or arbitrary
	meshed surfaces. The etymology of panorama suggests an overview,
	based on a choice of partially overlapping "pictures". We hope that
	this paper will contribute to the appreciation and apprehension of
	a stream of current research directions in image understanding.},
  doi = {DOI: 10.1016/j.sigpro.2011.04.025},
  issn = {0165-1684},
  owner = {duvall},
  timestamp = {2010.02.28},
  url = {http://www.sciencedirect.com/science/article/B6V18-52RR4XP-3/2/79bc3e4da8e86b67450190704480d111}
}
