Recent Reports
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2008

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Golden Oldies
2008
Fifteen Years of Reproducible Research in Computational Harmonic Analysis
with Arian Maleki, Morteza Shahram, Victoria Stodden, and Inam UrRahman.
Counting Faces of Randomly Projected Hypercubes and Orthants, with Applications
with Jared Tanner.
Exponential Bounds Implying Construction of Compressed Sensing Matrices, ErrorCorrecting Codes and Neighborly Polytopes by Random Sampling
with Jared Tanner.
Higher Criticism Thresholding: Optimal Feature Selection when Useful Features are Rare and Weak
with Jiashun Jin.
2007
Compressed Sensing MRI
with Michael Lustig and John Pauly.
Counting Faces of Randomly Projected Polytopes when the Projection Radically Lowers Dimension
with Jared Tanner.
2006
Fast Solution of L1 minimization problems when the solution may be sparse
with Yaacov Tsaig.
Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit
with Yaakov Tsaig, Iddo Drori, and JeanLuc Starck.
2005
Sparse Nonnegative Solutions of Underdetermined Linear Equations by Linear Programming
with Jared Tanner.
Neighborliness of RandomlyProjected Simplices in High Dimensions
with Jared Tanner.
Multiscale Representations of ManifoldValued Data
with Inam UrRaman, Iddo Drori, Victoria Stodden, and Peter Schroeder.
Neighborly Polytopes and Sparse Solutions of Underdetermined Linear Equations
HighDimensional Centrosymmetric Polytopes with Neighborliness Proportional to Dimension
2004
Extensions of Compressed Sensing
with Yaakov Tsaig.
Compressed Sensing
For Most Large Underdetermined Systems of Linear Equations, the minimal l1norm nearsolution approximates the sparsest nearsolution.
For Most Large Underdetermined Systems of Linear Equations, the minimal l1norm solution is also the sparsest solution.
Asymptotic Minimaxity of FDR Thresholding for Sparse Mixtures of Exponentials
with JiaShun Jin.
Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise
with Michael Elad and Vladimir Temlyakov.
ConnectTheDots: How many random points can a regular curve pass through?
with Ery AriasCastro, Xiaoming Huo, and Craig Tovey.
2003
Continuous Curvelet Transform I: Resolution of the Wavefront Set
with Emmanuel Candès.
Continuous Curvelet Transform II: Discretization and Frames
with Emmanuel Candès.
NearOptimal Detection of Geometric Objects by Fast Multiscale Methods
with Ery AriasCastro and Xiaoming Huo.
Adaptive Multiscale Detection of Filamentary Structures Embedded in Uniform Random Points
with Ery AriasCastro and Xiaoming Huo.
An InformationTheoretic Approach to Traffic Matrix Estimation
with with Carsten Lund, Matthew Roughan and Yin Zhang.
When does NonNegative Matrix Factorization Give a Correct Decomposition into Parts?
with Victoria Stodden
Hessian Eigenmaps: New LocallyLinear Embedding Techniques for HighDimensional Data
with Carrie Grimes
2002
New Tight Frames of Curvelets and Optimal Representations of Objects with C2 Singularities
with Emmanuel Candès
OptimallySparse Representation in General (nonOrthogonal) Dictionaries via l1 Minimization
with Michael Elad.
Multiscale SteppingStone Detection: Detecting Pairs of Jittered Interactive Streams by Exploiting Maximum Tolerable Delay
with Ana Georgina Flesia, Umesh Shankar Vern Paxson, Jason Coit, and Stuart Staniford.
When Does ISOMAP Recover the Natural Parameterization of Families of Articulated Images? (AKA: Image Manifolds which are Isometric to Euclidean Space)
with Carrie Grimes
Multiscale Geometric Analysis of 3D Galaxy Catalogues
with Ofer Levi, JeanLuc Starck, Vincent J. Martinez
Higher Criticism for Detecting Sparse Mixtures
with Jiashun Jin.
Digital Implementation of Ridgelet Packets
with Ana Georgina Flesia, Hagit HelOr, Amir Averbuch, Raphy Coifman, and Emmanuel Candès
Fast XRay and Beamlet Transforms for ThreeD Data
with Ofer Levi
The Kolmogorov Sampler
2001
Digital Ridgelet Transform based on true ridge functions
with Ana Georgina Flesia
Beamlets and Multiscale Image Processing
with Xiaoming Huo
Can Recent Developments in Harmonic Analysis `Explain' the Recent Findings in Natural Scene Statistics?
with Ana Georgina Flesia
Fast Slant Stack: A notion of Radon Transform for data on a Cartesian grid which is Rapidly Computable,Algebraically Exact, Geometrically Faithful, and Invertible
with A. Averbuch, R. Coifman, M. Israeli, and J. Walden
2000
Counting Bits with Kolmogorov and Shannon
Adapting to Unknown Sparsity by Controlling the False Discovery Rate
with Felix Abramovich, Yoav Benjamini, and Iain Johnstone
Curvelets and Curvilinear Integrals
with Emmanuel Candès
Recovering Edges in in IllPosed Linear Inverse Problems: Optimality of Curvelet Frames
with Emmanuel Candès
1999
Ridgelets: a key to higherdimensional intermittency?
with Emmanuel Candès
Uncertainty Principles and Ideal Atomic Decomposition
with Xiaoming Huo
Curvelets: A surprisingly effective nonadaptive representation of objects with edges
with Emmanuel Candès
Digital Curvelet Transform: Strategy, Implementation, Experiments
with Mark R. Duncan
1998
Ridge Functions and Orthonormal Ridgelets
kplane Ridgelets and the Problem of Representing objects which are smooth away from ddimensional
singularities in R^n
Sparse Components of Images and Optimal Atomic Decomposition
Data Compression and Harmonic Analysis.
with Martin Vetterli, Ron DeVore, and Ingrid Daubechies.
Orthonormal Ridgelets and Linear Singularities.
Smooth Multiwavelet Duals of Alpert Bases by MomentInterpolating Refinement
with Nira Dyn, David Levin, and Thomas PokYin Yu
Estimating Covariances of Locally Stationary Processes: Convergence of BestBasis Methods.
with Stéphane Mallat,and Rainer von Sachs.
1997
Asymptotic Minimaxity of Wavelet Shrinkage for Sampled Data.
with Iain Johnstone.
Fast Ridgelet Transform in Dimension 2.
(Not Currently Available)
Wedgelets: Nearly Minimax Estimation of Edges.
Nonlinear `Wavelet Transform' via MedianInterpolation.
with Thomas PokYin Yu.
1996
Renormalizing Experiments for Nonlinear Functionals
.
DeslauriersDubuc: Ten Years After.
with Thomas PokYin Yu.
Unconditional Bases and BitLevel Compression.
Wavelet Analysis
with Andrew Bruce and HongYe Gao
1995
"CART and BestOrthoBasis: a connection."
"Atomic Decomposition by Basis Pursuit."
with Scott Shaobing Chen and Michael Saunders.
"WaveLab and Reproducible Research."
with Jonathan Buckheit.
"TranslationInvariant DeNoising."
with Ronald R. Coifman.
1994
"Basis Pursuit."
with Scott Shaobing Chen
"Ideal Denoising in an Orthonormal Basis Chosen from a Library of Bases."
with Iain Johnstone.
"On Minimum Entropy Segmentation"
"NeoClassical Minimax Problems, Thresholding and Adaptation."
with Iain Johnstone.
Improved Linear Discrimination with a TimeFrequency Dictionary
with Jonathan Buckheit.
1993
"Smooth Wavelet Decompositions with Blocky Coefficient Kernels."
"Wavelet Shrinkage and W.V.D.  A TenMinute Tour."
with
figures.
"Adapting to Unknown Smoothness via Wavelet Shrinkage."
with Iain Johnstone.
"Density Estimation by Wavelet Thresholding."
with Iain Johnstone, Gérard Kerkyacharian, and Dominique Picard.
"Wavelet Shrinkage: Asymptopia."
with Iain Johnstone, Gérard Kerkyacharian, and Dominique Picard.
"Nonlinear Wavelet Methods for Recovering Signals, Images, and Densities from indirect and noisy data."
with archive of
figures
.
1992
"DeNoising via Soft Thresholding."
"Interpolating Wavelet Transforms."
"Nonlinear Solution of Linear Inverse Problems by WaveletVaguelette Decomposition"
"Unconditional Bases are Optimal Bases for Data Compression and for Statistical Estimation"
"Ideal Spatial Adaptation via Wavelet Shrinkage."
With
figures.
with Iain Johnstone.
"Minimax Estimation via Wavelet Shrinkage."
with Iain Johnstone.
"Minimax Risk Over $l_p$Balls for $l_q$Error."
with Iain Johnstone.
2003

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Golden Oldies
© Dave Donoho 2002