Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Journal of Complexity
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Near-optimal sparse fourier representations via sampling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
A generalized uncertainty principle and sparse representation in pairs of bases
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution
Signal Processing - Sparse approximations in signal and image processing
Bayesian compressive sensing and projection optimization
Proceedings of the 24th international conference on Machine learning
Multi-task compressive sensing with Dirichlet process priors
Proceedings of the 25th international conference on Machine learning
Compressive light transport sensing
ACM Transactions on Graphics (TOG)
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Compressive sensing for multi-static scattering analysis
Journal of Computational Physics
Wavelet-based acoustic detection of moving vehicles
Multidimensional Systems and Signal Processing
IEEE Transactions on Signal Processing
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
Practical compressive sensing of large images
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Recovering sparse signals with a certain family of nonconvex penalties and DC programming
IEEE Transactions on Signal Processing
Image representation by compressive sensing for visual sensor networks
Journal of Visual Communication and Image Representation
An application of compressive sensing for image fusion
Proceedings of the ACM International Conference on Image and Video Retrieval
Compressed sensing for synthetic aperture radar imaging
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
IEEE Transactions on Signal Processing
Bayesian compressive sensing using Laplace priors
IEEE Transactions on Image Processing
Sparse representation of medical images via compressed sensing using Gaussian scale mixtures
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Image compressed sensing based on wavelet transform in contourlet domain
Signal Processing
Two-dimensional random projection
Signal Processing
A coordinate gradient descent method for l1-regularized convex minimization
Computational Optimization and Applications
A Bayesian Lasso via reversible-jump MCMC
Signal Processing
Robust ISAR imaging based on compressive sensing from noisy measurements
Signal Processing
Compressed sensing meets the human visual system
ICHIT'11 Proceedings of the 5th international conference on Convergence and hybrid information technology
Combinatorial algorithms for compressed sensing
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Compressive rendering of multidimensional scenes
Proceedings of the 2010 international conference on Video Processing and Computational Video
Block-Based Compressed Sensing of Images and Video
Foundations and Trends in Signal Processing
Adaptive Compressed Image Sensing Using Dictionaries
SIAM Journal on Imaging Sciences
Compressed sampling for heart rate monitoring
Computer Methods and Programs in Biomedicine
The method for constructing block sparse measurement matrix based on orthogonal vectors
PCM'12 Proceedings of the 13th Pacific-Rim conference on Advances in Multimedia Information Processing
Performance analysis of partial segmented compressed sampling
Signal Processing
Compressed sensing-based MRI reconstruction using complex double-density dual-tree DWT
Journal of Biomedical Imaging
Image representation using block compressive sensing for compression applications
Journal of Visual Communication and Image Representation
Compressed classification learning with Markov chain samples
Neural Networks
Stationary-sparse causality network learning
The Journal of Machine Learning Research
Recurrent networks for compressive sampling
Neurocomputing
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We study the notion of compressed sensing (CS) as put forward by Donoho, Candes, Tao and others. The notion proposes a signal or image, unknown but supposed to be compressible by a known transform, (e.g. wavelet or Fourier), can be subjected to fewer measurements than the nominal number of data points, and yet be accurately reconstructed. The samples are nonadaptive and measure 'random' linear combinations of the transform coefficients. Approximate reconstruction is obtained by solving for the transform coefficients consistent with measured data and having the smallest possible l1 norm.We present initial 'proof-of-concept' examples in the favorable case where the vast majority of the transform coefficients are zero. We continue with a series of numerical experiments, for the setting of lp-sparsity, in which the object has all coefficients nonzero, but the coefficients obey an lp bound, for some p ∈ (0, 1]. The reconstruction errors obey the inequalities paralleling the theory, seemingly with well-behaved constants.We report that several workable families of 'random' linear combinations all behave equivalently, including random spherical, random signs, partial Fourier and partial Hadamard.We next consider how these ideas can be used to model problems in spectroscopy and image processing, and in synthetic examples see that the reconstructions from CS are often visually "noisy". To suppress this noise we postprocess using translation-invariant denoising, and find the visual appearance considerably improved.We also consider a multiscale deployment of compressed sensing, in which various scales are segregated and CS applied separately to each; this gives much better quality reconstructions than a literal deployment of the CS methodology.These results show that, when appropriately deployed in a favorable setting, the CS framework is able to save significantly over traditional sampling, and there are many useful extensions of the basic idea.