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Signal processing, multiscale image analysis and graph-inference
Codes & Matlab toolboxes

Oversampled Filter Banks | Dual-Tree wavelets | FFT | Bijections
Graph Inference | Sparse Trend/Background/Baseline | Sparse Blind Deconvolution

Optimal oversampled Complex Filter Banks synthesis toolbox and SURE-LET (Stein-based e) denoising (Matlab toolbox code)

Oversampled Synthesis Filter Banks matlab toolbox toolset Filter Bank generation (FB_gen) toolbox: Synthesis of Optimized Oversampled Inverse Filter Banks, given "almost any" real or complex analysis oversampled filter bank this toolbox offers some tools to build and optimize real or complex inverse oversampled filter banks.
Stein principle based denoising with filter banks: FB-SURE-LET-S and FB-SURE-LET-C Sure-LET denoising toolbox: this toolbox performs denoising of images using the FB-SURE-LET-S and FB-SURE-LET-C methods, with two-dimensional oversampled, directional filter banks and Stein Unbiaised Risk Estimation for LInear Expansion of Threshold. Some functions require the FB_gen toolbox
COLT toolbox: Complex Oversampled Lapped Transform toolbox for time-frequency analysis/synthesis and spectrogram processing COLT toolbox: Complex Oversampled Lapped Transform toolbox for time-frequency analysis/synthesis and spectrogram processing (coming in 2017?)
Author: Jérôme Gauthier (CEA, formerly Telecom Paris Tech). PhD thesis (thèse de doctorat): Analyse de signaux et d’images par bancs de filtres. Applications aux géosciences (on complex oversampled filter banks with geoscience applications)

Matlab codes were created to illustrate the results presented in some of Jérôme Gauthier papers on optimization of multirate "oversampled filter banks" for denoising and image analysis purposes. You can use them freely for research purposes, as long as the following paper is credited (successfully tested with Matlab 2007b for windows):

Optimization of Synthesis Oversampled Complex Filter Banks (DOI:10.1109/TSP.2009.2023947, HAL)
Jérôme Gauthier, Laurent Duval and Jean-Christophe Pesquet
IEEE Transactions on Signal Processing, October 2009, Volume 57, Issue 10, p. 3827-3843

Dual-Tree Wavelets (M-band or multiband): application to multivariate image Denoising, with multiscale block SURE based on Stein's Unbiased Risk Estimator principle (Matlab code)

Author: Caroline Chaux (Université Aix-Marseille, formerly Université Paris-Est)
A nonlinear Stein-based estimator for multichannel image denoising matlab toolbox [MatlabCentral: M-band 2D dual-tree (Hilbert) wavelet multicomponent image denoising]+[Local Matlab version]+[precompiled coded version]

Matlab codes were created to illustrate the results presented in some of Caroline Chaux papers. You can use them freely for research purposes, as long as the following papers are credited (successfully tested with Matlab 2007b for windows):

A nonlinear Stein-based estimator for multichannel image denoising (DOI:10.1109/TSP.2008.921757, Arxiv )
Caroline Chaux, Laurent Duval, Amel Benazza-Benyahia and Jean-Christophe Pesquet
IEEE Transactions on Signal Processing, August 2008, Volume 56, Issue 8, p. 3855-3870
Noise covariance properties in dual-tree wavelet decompositions (DOI:10.1109/TIT.2007.909104 )
Caroline Chaux, Jean-Christophe Pesquet and Laurent Duval
IEEE Transactions on Information Theory, December 2007, Volume 53, Issue 12, p. 4680-4700
Image analysis using a dual-tree M-band wavelet transform (DOI:10.1109/TIP.2006.875178)
Caroline Chaux, Laurent Duval and Jean-Christophe Pesquet
IEEE Transactions on Image Processing, August 2006, Volume 15, Issue 8, p. 2397-2412

FFT (fast Fourier transform) Matlab code

Author: Laurent Duval (IFP Energies nouvelles)
Amplitude corrected m-file for computing/displaying the FFT of real signals Amplitude corrected m-file for computing/displaying the FFT of real signals

N > N^2 and N^2 > N bijections or pairing functions via Cantor polynomials, Square or Power-Of-Two-Odd

Author: Laurent Duval (IFP Energies nouvelles)
Three different bijections or pairing functions between N and N^2 (including Cantor polynomials) Three different bijections or pairing functions between N and N^2 (including Cantor polynomials)
Bijection_Pairing_N_N2(index_In,flag_Pair) provides three different explicit bijections between [0,...,K] and some consistently growing (Cantor or triangle, Elegant or square, Power-Of-Two-Odd or POTO for 2-adic integer decomposition) subset of N^2. It allows different strategies to wander across a set of two-dimensional integer coordinates.
The most famous pairing functions between N and N^2 are Cantor polynomials: = ((x+y)^2+x+3y)/2 or = ((x+y)^2+3x+y)/2). Whether they are the only bijective polynomials (between N and N^2) remains an open question. They parse the positive quadrant along parallel, anti-diagonal lines, starting from the (0,0) origin. The indices increase as growing triangles, following an l_1 norm, i.e. the sum of x and y is piece-wise constant and non-decreasing. It is given by: flag_Pair = 'Cantor' or 'c'.
A second pairing function grows in concentric squares. It elegantly mimics a max or l_infinity norm, with = x+(y+floor((x+1)/2))^2. It is given by: flag_Pair = 'Elegant' or 'e'. 'Cantor' and 'Elegant' pairing are relatively symmetric around the main diagonal.
The third and last one (POTO pairing) is more asymmetric. It can be used when one index should grow quicker than the other (roughly hyperbolic). It is related to the 2-adic representation, or the decomposition of an integer into the product of a power of two and an odd number (Power-Of-Two-Odd). It corresponds to: = 2^x*(2*y-1) - 1. It is given by: flag_Pair = 'Elegant' or 'e'. Without output argument, the code displays the competition between 'Cantor', 'Elegant' and 'POTO', up to the first integer both triangular and square: 36 (not 42, to my infinite sadness).
The bijection order is given by the dimension (1 or 2) of the input index. A few references are provided for implementing pairing functions in higher dimensions.

BRANE Cut: Graph Inference for Gene Regulatory Networks

Author: Aurélie Pirayre, IFP Energies nouvelles
BRANE Cut: Biologically-Related Apriori Network Enhancement with Graph cuts for Gene Regulatory Network Inference BRANE Cut: Biologically-Related Apriori Network Enhancement with Graph cuts for Gene Regulatory Network Inference

BEADS: Baseline Estimation And Denoising with Sparsity

Author: Xiaoran Ning
Chromatogram baseline estimation and denoising using sparsity (BEADS) (on background estimation or baseline removal for analytic chemistry signals) Chromatogram baseline estimation and denoising using sparsity (BEADS) (on background estimation or baseline removal for analytic chemistry signals) http://lc.cx/beads
Chromatogram baseline estimation and denoising using sparsity (BEADS) (DOI:10.1016/j.chemolab.2014.09.014)
Xiaoran Ning, Ivan Selesnick, Laurent Duval
Chemometrics and Intelligent Laboratory Systems, p. 156-167, Volume 139, December 2014
This paper jointly addresses the problems of chromatogram baseline correction and noise reduction. The proposed approach is based on modeling the series of chromatogram peaks as sparse with sparse derivatives, and on modeling the baseline as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty functions is utilized. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. See paper page

SOOT: Sparse blind deconvolution with Smooth l_1/l_2 norm ratio

Author: Audrey Repetti, Mai Quyen Pham
SOOT: Sparse blind deconvolution with Smooth l_1/l_2 norm (Smooth-One-Over-Two) ratio SOOT: Sparse blind deconvolution with Smooth l_1/l_2 norm (Smooth-One-Over-Two) ratio http://lc.cx/soot
Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l_1/l_2 Regularization (or SOOT, for Smoothed One-Over-Two norm ratio) (DOI:10.1109/LSP.2014.2362861)
Audrey Repetti, Mai Quyen-Pham, Laurent Duval, Émilie Chouzenoux, Jean-Christophe Pesquet
IEEE Signal Processing Letters, May 2015
The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution.


For those looking for "matlab codes for ieee papers", we salute you