Linear inversion of ban limit reflection seismograms
SIAM Journal on Scientific and Statistical Computing
Visual reconstruction
Uncertainty principles and signal recovery
SIAM Journal on Applied Mathematics
Ten lectures on wavelets
Superresolution via sparsity constraints
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Signal recovery and the large sieve
SIAM Journal on Applied Mathematics
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
SIAM Journal on Applied Mathematics
Stable multiscale bases and local error estimation for elliptic problems
Applied Numerical Mathematics - Special issue on multilevel methods
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Composite wavelet bases for operator equations
Mathematics of Computation
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Adaptive Wavelet Methods for Saddle Point Problems---Optimal Convergence Rates
SIAM Journal on Numerical Analysis
Convergence of Adaptive Finite Element Methods
SIAM Review
Hybrid representations for audiophonic signal encoding
Signal Processing - Image and Video Coding beyond Standards
Wavelets and curvelets for image deconvolution: a combined approach
Signal Processing - Special section: Security of data hiding technologies
Adaptive Wavelet Schemes for Nonlinear Variational Problems
SIAM Journal on Numerical Analysis
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
Adaptive Wavelet Galerkin Methods for Linear Inverse Problems
SIAM Journal on Numerical Analysis
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
An Optimal Adaptive Finite Element Method
SIAM Journal on Numerical Analysis
Adaptive Solution of Operator Equations Using Wavelet Frames
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Optimality of a Standard Adaptive Finite Element Method
Foundations of Computational Mathematics
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
SIAM Journal on Numerical Analysis
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Subspace Correction Methods for Total Variation and $\ell_1$-Minimization
SIAM Journal on Numerical Analysis
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
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This paper is concerned with an overview of the main concepts and a few significant applications of a class of adaptive iterative algorithms which allow for dimensionality reductions when used to solve large scale problems. We call this class of numerical methods Compressive Algorithms . The introduction of this paper presents an historical excursus on the developments of the main ideas behind compressive algorithms and stresses the common features of diverse applications. The first part of the paper is addressed to the optimal performances of such algorithms when compared with known benchmarks in the numerical solution of elliptic partial differential equations. In the second part we address the solution of inverse problems both with sparsity and compressibility constraints. We stress how compressive algorithms can stem from variational principles. We illustrate the main results and applications by a few significant numerical examples. We conclude by pointing out future developments.