Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Random projection in dimensionality reduction: applications to image and text data
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Biometrics, Personal Identification in Networked Society: Personal Identification in Networked Society
Atomic Decomposition by Basis Pursuit
SIAM Review
An elementary proof of a theorem of Johnson and Lindenstrauss
Random Structures & Algorithms
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Two-Stage Linear Discriminant Analysis via QR-Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized Low Rank Approximations of Matrices
Machine Learning
A simple test to check the optimality of a sparse signal approximation
Signal Processing - Sparse approximations in signal and image processing
On the stability of the basis pursuit in the presence of noise
Signal Processing - Sparse approximations in signal and image processing
Extensions of compressed sensing
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Two dictionaries matching pursuit for sparse decomposition of signals
Signal Processing - Special section: Distributed source coding
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Random Projections of Smooth Manifolds
Foundations of Computational Mathematics
Toeplitz-Structured Compressed Sensing Matrices
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Robust-SL0 for stable sparse representation in noisy settings
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Sparse decomposition of two dimensional signals
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
A fast approach for overcomplete sparse decomposition based on smoothed l0 norm
IEEE Transactions on Signal Processing
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
Two dimensional compressive classifier for sparse images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Sampling signals with finite rate of innovation
IEEE Transactions on Signal Processing
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
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As an alternative to adaptive nonlinear schemes for dimensionality reduction, linear random projection has recently proved to be a reliable means for high-dimensional data processing. Widespread application of conventional random projection in the context of image analysis is, however, mainly impeded by excessive computational and memory requirements. In this paper, a two-dimensional random projection scheme is considered as a remedy to this problem, and the associated key notion of concentration of measure is closely studied. It is then applied in the contexts of image classification and sparse image reconstruction. Finally, theoretical results are validated within a comprehensive set of experiments with synthetic and real images.