Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Stochastic models for generic images
Quarterly of Applied Mathematics
On Advances in Statistical Modeling of Natural Images
Journal of Mathematical Imaging and Vision
Dictionary learning algorithms for sparse representation
Neural Computation
DCC '00 Proceedings of the Conference on Data Compression
Learning Overcomplete Representations
Neural Computation
Self-taught learning: transfer learning from unlabeled data
Proceedings of the 24th international conference on Machine learning
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Compression of facial images using the K-SVD algorithm
Journal of Visual Communication and Image Representation
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Optimized Projections for Compressed Sensing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Sparse representations in unions of bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
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
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
IEEE Transactions on Signal Processing
Optimized projection matrix for compressive sensing
EURASIP Journal on Advances in Signal Processing
Nonlinear nearest subspace classifier
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Image deblocking via sparse representation
Image Communication
Dictionary Learning for Noisy and Incomplete Hyperspectral Images
SIAM Journal on Imaging Sciences
Compressive light field photography using overcomplete dictionaries and optimized projections
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Sparse signal reconstruction using decomposition algorithm
Knowledge-Based Systems
Online dictionary learning algorithm with periodic updates and its application to image denoising
Expert Systems with Applications: An International Journal
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Sparse signal representation, analysis, and sensing have received a lot of attention in recent years from the signal processing, optimization, and learning communities. On one hand, learning overcomplete dictionaries that facilitate a sparse representation of the data as a liner combination of a few atoms from such dictionary leads to state-of-the-art results in image and video restoration and classification. On the other hand, the framework of compressed sensing (CS) has shown that sparse signals can be recovered fromfar less samples than those required by the classical Shannon-Nyquist Theorem. The samples used in CS correspond to linear projections obtained by a sensing projection matrix. It has been shown that, for example, a nonadaptive random sampling matrix satisfies the fundamental theoretical requirements of CS, enjoying the additional benefit of universality. On the other hand, a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy or further reduce the necessary number of samples. In this paper, we introduce a framework for the joint design and optimization, from a set of training images, of the nonparametric dictionary and the sensing matrix. We show that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary. Particular cases of the proposed framework include the optimization of the sensing matrix for a given dictionary as well as the optimization of the dictionary for a predefined sensing environment. The presentation of the framework and its efficient numerical optimization is complemented with numerous examples on classical image datasets.