Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Model-based compressive sensing for signal ensembles
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Reconstruction From Noisy Random Projections
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
IEEE Transactions on Image Processing
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Block-sparse signals: uncertainty relations and efficient recovery
IEEE Transactions on Signal Processing
Sparsity-regularized photon-limited imaging
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Enhancement of coupled multichannel images using sparsity constraints
IEEE Transactions on Image Processing
ADMiRA: atomic decomposition for minimum rank approximation
IEEE Transactions on Information Theory
Compressive acquisition of dynamic scenes
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Sparse Signal Reconstruction via Iterative Support Detection
SIAM Journal on Imaging Sciences
K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance
Proceedings of the forty-third annual ACM symposium on Theory of computing
Proximal Methods for Hierarchical Sparse Coding
The Journal of Machine Learning Research
Bayesian compressive sensing for cluster structured sparse signals
Signal Processing
Sparse recovery with partial support knowledge
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Sparsity Driven People Localization with a Heterogeneous Network of Cameras
Journal of Mathematical Imaging and Vision
Compressed sensing meets the human visual system
ICHIT'11 Proceedings of the 5th international conference on Convergence and hybrid information technology
Convex and Network Flow Optimization for Structured Sparsity
The Journal of Machine Learning Research
Structured Variable Selection with Sparsity-Inducing Norms
The Journal of Machine Learning Research
Learning with Structured Sparsity
The Journal of Machine Learning Research
Pattern Recognition Letters
Efficient sketches for the set query problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Structured sparse linear graph embedding
Neural Networks
Extracting non-negative basis images using pixel dispersion penalty
Pattern Recognition
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Block-Based Compressed Sensing of Images and Video
Foundations and Trends in Signal Processing
Structured sparsity and generalization
The Journal of Machine Learning Research
Adaptive Compressed Image Sensing Using Dictionaries
SIAM Journal on Imaging Sciences
SAR image reconstruction and autofocus by compressed sensing
Digital Signal Processing
K-sparse approximation for traffic histogram dimensionality reduction
Proceedings of the 8th International Conference on Network and Service Management
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
A learning-based method for compressive image recovery
Journal of Visual Communication and Image Representation
Image representation using block compressive sensing for compression applications
Journal of Visual Communication and Image Representation
Greedy feature selection for subspace clustering
The Journal of Machine Learning Research
Hi-index | 754.91 |
Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K ≪ N elements from an N-dimensional basis. Instead of taking periodic samples, CS measures inner products with M N random vectors and then recovers the signal via a sparsity-seeking optimization or greedy algorithm. Standard CS dictates that robust signal recovery is possible from M = O(K log (N/K)) measurements. It is possible to substantially decrease M without sacrificing robustness by leveraging more realistic signal models that go beyond simple sparsity and compressibility by including structural dependencies between the values and locations of the signal coefficients. This paper introduces a model-based CS theory that parallels the conventional theory and provides concrete guidelines on how to create model-based recovery algorithms with provable performance guarantees. A highlight is the introduction of a new class of structured compressible signals along with a new sufficient condition for robust structured compressible signal recovery that we dub the restricted amplification property, which is the natural counterpart to the restricted isometry property of conventional CS. Two examples integrate two relevant signal models--wavelet trees and block sparsity--into two state-of-the-art CS recovery algorithms and prove that they offer robust recovery from just M = O(K) measurements. Extensive numerical simulations demonstrate the validity and applicability of our new theory and algorithms.