# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
5002 History And Philosophy Of Specific Fields

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4603 Computer Vision And Multimedia Computation

# keywords[]
4603 Computer Vision And Multimedia Computation

# educationAndTraining[].organization.label
The Ohio State University - (Columbus, Ohio, United States)

# educationAndTraining[].organization.label
Eastern Michigan University - (Ypsilanti, Michigan, United States)

# publications[].label
Convex polynomial and spline approximation inLp, O<p<

# publications[].label
Error Bounds for Gaussian Quadrature and Weighted-$L^1$ Polynomial Approximation

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
On the construction of multivariate (pre)wavelets

# publications[].label
Data assimilation and sampling in Banach spaces

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Optimal entropy encoders for mining multiply resolved data

# publications[].label
Fast computation in adaptive tree approximation

# publications[].label
Recovery of an initial temperature from discrete sampling

# publications[].label
Minimum moduli of differential operators from the viewpoint of approximation theory

# publications[].label
Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients

# publications[].label
Convex Polynomial Approximation in Lp (0 < p < 1)

# publications[].label
Deterministic constructions of compressed sensing matrices

# publications[].label
Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs

# publications[].label
Capturing Ridge Functions in High Dimensions from Point Queries

# publications[].label
On polynomials of best one-sided approximation

# publications[].label
Convergence Rates for Greedy Algorithms in Reduced Basis Methods

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Wavelet compression and segmentation of digital mammograms.

# publications[].label
Compressed sensing and best k k -term approximation

# publications[].label
Effect of wavelet bases on compressing digital mammograms

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Sparse Evaluation of Compositions of Functions Using Multiscale Expansions

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A/D Conversion With Imperfect Quantizers

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Freud's work in constructive function theory

# publications[].label
Approximation of high-dimensional parametric PDEs *

# publications[].label
Saturation of positive convolution operators

# publications[].label
Nonlinear approximation and the space BV (2)

# publications[].label
The Approximation of Continuous Functions by Positive Linear Operators

# publications[].label
Nonlinear approximation and its applications

# publications[].label
Smoothness spaces and wavelet decomposition (Invited Paper)

# publications[].label
Multiscale Characterizations of Besov Spaces on Bounded Domains

# publications[].label
Approximation from shift-invariant subspaces of L 2 ( R d ) L_ 2(mathbf {R}^ d)

# publications[].label
The Structure of Finitely Generated Shift-Invariant Spaces in L2(Rd)

# publications[].label
Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations

# publications[].label
Besov regularity for elliptic boundary value problems

# publications[].label
Kolmogorov widths under holomorphic mappings

# publications[].label
ADAPTIVE FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS WITH DISCONTINUOUS COEFFICIENTS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Maximal Spaces with Given Rate of Convergence for Thresholding Algorithms

# publications[].label
Adaptive Wavelet Methods IIBeyond the Elliptic Case

# publications[].label
Multiscale decompositions on bounded domains

# publications[].label
Adaptive Wavelet Schemes for Nonlinear Variational Problems

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Error analysis for piecewise quadratic curve fitting algorithms

# publications[].label
Adaptive wavelet methods for elliptic operator equations: Convergence rates

# publications[].label
Motion Estimation With the Redundant Wavelet Transform

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Nonlinear Approximation by Trigonometric Sums

# publications[].label
Universal algorithms for learning theory part I: Piecewise constant functions

# publications[].label
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

# publications[].label
Using nonlinear wavelet compression to enhance image registration

# publications[].label
DIFFUSION COEFFICIENTS ESTIMATION FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Approximation Methods for Supervised Learning

# publications[].label
Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage.

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order

# publications[].label
ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S

# publications[].label
On the differentiability of functions in R n 	extbf {R}^{n}

# publications[].label
On the Size and Smoothness of Solutions to Nonlinear Hyperbolic Conservation Laws

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Approximation Orders of FSI Spaces in L2(Rd)

# publications[].label
Vision-based control of micro-air-vehicles: Progress and problems in estimation

# publications[].label
Tensor-Sparsity of Solutions to High-Dimensional Elliptic Partial Differential Equations

# publications[].label
Approximation using scattered shifts of a multivariate function

# publications[].label
Beta expansions: a new approach to digitally corrected A/D conversion

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Approximation of Functions of Few Variables in High Dimensions

# publications[].label
Approximation Orders of FSI Spaces in L2(Rd)

# publications[].label
Wavelet compression of three-dimensional time-lapse biological image data.

# publications[].label
Adaptive Finite Element Methods with convergence rates

# publications[].label
Multiscale, Nonlinear and Adaptive Approximation

# publications[].label
Classifying the smoothness of images: theory and applications to wavelet image processing

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Approximation and learning by greedy algorithms

# publications[].label
Iteratively Re-weighted Least Squares minimization: Proof of faster than linear rate for sparse recovery

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Saturation theorems for discretized linear operators

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Anisotropic smoothness spaces via level sets

# publications[].label
Besov spaces on domains in R d 	extbf {R}^ d

# publications[].label
Orthogonal Matching Pursuit Under the Restricted Isometry Property

# publications[].label
Iteratively reweighted least squares minimization for sparse recovery

# publications[].label
Approximation of High-Dimensional Rank One Tensors

# publications[].label
Image compression through wavelet transform coding

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Tree approximation of the long wave radiation parameterization in the NCAR CAM global climate model

# publications[].label
The degree of approximation by Chebyshevian splines

# publications[].label
Universal Algorithms for Learning Theory. Part II: Piecewise Polynomial Functions

# publications[].label
Greedy wavelet projections are bounded on BV

# publications[].label
Approximation by smooth multivariate splines

# publications[].label
Greedy Algorithms for Reduced Bases in Banach Spaces

# publications[].label
Instance-optimality in probability with an 1-minimization decoder

# publications[].label
A Simple Proof of the Restricted Isometry Property for Random Matrices

# publications[].label
Pointwise estimates for monotone polynomial approximation

# publications[].label
Best Basis Selection for Approximation in Lp

# publications[].label
A geometric proof of total positivity for spline interpolation

# publications[].publisher
SPIE, the international society for optics and photonics

# researcherOn[].label
Numerical Methods for Solving Parametric PDEs

# researcherOn[].awardedBy.label
United States Department of the Navy - (Arlington, Virginia, United States)

# researcherOn[].label
Numerical Methods for Parametric Partial Differential Equations

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Data Assimilation and Parameter Estimation for Parametric Partial Differential Equations

# researcherOn[].awardedBy.label
United States Department of the Navy - (Arlington, Virginia, United States)

# researcherOn[].label
Computation and Learning In High Dimensions

# researcherOn[].awardedBy.label
United States Department of the Navy - (Arlington, Virginia, United States)

# researcherOn[].label
Atd Collaborative Research: Theory and Algorithms for High Dimensional Learning

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
The Numerical Recovery of High Dimensional Functions

# researcherOn[].awardedBy.label
United States Department of the Navy - (Arlington, Virginia, United States)

# researcherOn[].label
HDR Tripods: Texas A&M Research Institute for Interdisciplinary Foundations of DATA Science (TRIFECDAS)

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
High Performance Computational Structure For Parameter Estimations of Parametric Partial Differential Equations

# researcherOn[].awardedBy.label
United States Department of the Navy - (Arlington, Virginia, United States)

# researcherOn[].label
Numerical Methods for High Dimensional Partial Differential Equations

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# inTheNews[].label
Texas A&M Chemist Karen Wooley Elected To National Academy Of Sciences