Nonstationary subdivision schemes and multiresolution analysis
SIAM Journal on Mathematical Analysis
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Surface compression with geometric bandelets
ACM SIGGRAPH 2005 Papers
Extensions of compressed sensing
Signal Processing - Sparse approximations in signal and image processing
Computation of the Fast Walsh-Fourier Transform
IEEE Transactions on Computers
Non-local Regularization of Inverse Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Manifold models for signals and images
Computer Vision and Image Understanding
Random Projections of Smooth Manifolds
Foundations of Computational Mathematics
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
IEEE Transactions on Image Processing
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Model-based compressive sensing
IEEE Transactions on Information Theory
Optimized Projections for Compressed Sensing
IEEE Transactions on Signal Processing
Decoding by linear programming
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
Compressed Sensing and Redundant Dictionaries
IEEE Transactions on Information Theory
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
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This paper proposes a best basis extension of compressed sensing recovery. Instead of regularizing the compressed sensing inverse problem with a sparsity prior in a fixed basis, our framework makes use of sparsity in a tree-structured dictionary of orthogonal bases. A new iterative thresholding algorithm performs both the recovery of the signal and the estimation of the best basis. The resulting reconstruction from compressive measurements optimizes the basis to the structure of the sensed signal. Adaptivity is crucial to capture the regularity of complex natural signals. Numerical experiments on sounds and geometrical images indeed show that this best basis search improves the recovery with respect to fixed sparsity priors.