Compressed Sensing
This page contains resources about Compressed Sensing, Sparse Sampling and Sparse Signal Processing.
Subfields and ConceptsEdit
- Incoherence / Incoherent Sampling / Incoherent bases
- Canonical/Kroneker basis
- Fourier basis
- Random basis
- Random sequences / codes
- Inverse Discrete Cosine Transform (IDCT) / Heisenberg
- Wavelet basis
- Coherent-based Sampling
- Coherence / Mutual Coherence
- Local Coherence
- Null Space Property
- Restricted Isometry Property
- Underdetermined Linear System
- Uncertainty Principles (between sparsity basis and measurement system)
- Continuous Uncertainty Principles (Heisenberg)
- Discrete Uncertainty Principle (Donoho and Stark)
- Dirac Comb / Picket Fence
- Quantitative Uncertainty Principle
- Quantitative Robust Uncertainty Principle
- Sparse Approximation / Sparse Representation
- Basis Pursuit
- Matching Pursuit
- Sparse Signal Recovery / Sparse Signal Reconstruction
- Exact Recovery Theorem
- Stable Recovery / Stability Theorem
- Sub-Nyquist Sampling
- Nonlinear Sampling Theorem
- Iterative Reweighted Least Squares
- Sparse Principal Component Analysis (PCA)
- Structure Sparse PCA
- B-Splines
- E-Splines
- Wavelets
- Bayesian Compressive Sensing
- Variational Bayesian Compressive Sensing
- Sparse Bayesian Models
- Inverse Problems (Optimization)
- Regularization
- Regularized least squares
- L0 penalization / Spike-and-slab prior
- L1-regularization / LASSO / Laplace prior
- L2-regularization / Ridge Regression / Gaussian prior
- Elastic nets
- Total Variation (TV) Regularization (i.e. L1-norm of the gradient)
- Regularization
Online CoursesEdit
Video LecturesEdit
Lecture NotesEdit
Books and Book ChaptersEdit
- Theodoridis, S. (2015). "Chapter 9: Sparsity-Aware Learning". Machine Learning: A Bayesian and Optimization Perspective. Academic Press.
- Hastie, T., Tibshirani, R., & Wainwright, M. (2015). "Chapter 10: Signal Approximation and Compressed Sensing". Statistical learning with sparsity: the lasso and generalizations. CRC Press.
- Eldar, Y. C. (2015). Sampling theory: Beyond bandlimited systems. Cambridge University Press.
- Carmi, A. Y., L. Mihaylova, & S. J. Godsill (Eds.). (2014). Compressed Sensing and Sparse Filtering. Springer.
- Rish, I., & Grabarnik, G. (2014). Sparse modeling: theory, algorithms, and applications. CRC Press.
- Foucart, S., & Rauhut, H. (2013). A mathematical introduction to compressive sensing. Birkhäuser.
- Murphy, K. P. (2012). "Chapter 13: Sparse linear models". Machine Learning: A Probabilistic Perspective. MIT Press.
- Baraniuk, R., Davenport, M. A., Duarte, M. F., & Hegde, C. (2011). An introduction to compressive sensing. Connexions e-textbook.
- Starck, J. L., Murtagh, F., & Fadili, J. M. (2010). "Chapter 11: Compressed Sensing". Sparse image and signal processing: wavelets, curvelets, morphological diversity. Cambridge University Press.
- Elad, M. (2010). Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer.
- Mallat, S. (2008). A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press.
- Saad, Y. (2003). Iterative Methods for Sparse Linear Systems. Siam.
- MacKay, D. J. (2003). "Part VI: Sparse Graph Codes". Information Theory, Inference and Learning Algorithms. Cambridge University Press.
Scholarly ArticlesEdit
- Chen, Y., Bhojanapalli, S., Sanghavi, S., & Ward, R. (2014). Coherent matrix completion. In Proceedings of the 31st International Conference on Machine Learning (pp. 674-682).
- Davenport, M. A., Duarte, M. F., Eldar, Y. C., & Kutyniok, G. (2011). Introduction to compressed sensing. Preprint, 93(1), 2.
- Fornasier, M., & Rauhut, H. (2011). Compressive sensing. In Handbook of mathematical methods in imaging (pp. 187-228). Springer New York.
- Yang, J., Wright, J., Huang, T. S., & Ma, Y. (2010). Image super-resolution via sparse representation. IEEE Transactions on image processing, 19(11), 2861-2873.
- Dai, W., & Milenkovic, O. (2009). Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory, 55(5), 2230-2249.
- Starck, J. L., & Fadili, M. J. (2009). An overview of inverse problem regularization using sparsity. In Image Processing (ICIP), 16th IEEE International Conference on, 1453-1456.
- Duarte, M. F., Davenport, M. A., Takhar, D., Laska, J. N., Sun, T., Kelly, K. E., & Baraniuk, R. G. (2008). Single-pixel imaging via compressive sampling.IEEE Signal Processing Magazine, 25(2), 83.
- Ji, S., Xue, Y., & Carin, L. (2008). Bayesian compressive sensing. IEEE Transactions on Signal Processing, 56(6), 2346-2356.
- Candès, E. J., & Wakin, M. B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21-30.
- Blu, T., Dragotti, P. L., Vetterli, M., Marziliano, P., & Coulot, L. (2008). Sparse sampling of signal innovations. IEEE Signal Processing Magazine, 25(2), 31-40.
- Lustig, M., Donoho, D. L., Santos, J. M., & Pauly, J. M. (2008). Compressed sensing MRI. IEEE Signal Processing Magazine, 25(2), 72-82.
- Lustig, M., Donoho, D., & Pauly, J. M. (2007). Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic resonance in medicine, 58(6), 1182-1195.
- Dragotti, P. L., Vetterli, M., & Blu, T. (2007). Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strang–Fix.IEEE Transactions on Signal Processing, 55(5), 1741-1757.
- Baraniuk, R. G. (2007). Compressive sensing. IEEE Signal Processing Magazine, 24(4).
- Candes, E., & Romberg, J. (2007). Sparsity and incoherence in compressive sampling. Inverse problems, 23(3), 969.
- Candes, E. J., Romberg, J., & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information.IEEE Transactions on information theory, 52(2), 489-509.
- Candes, E. J., Romberg, J. K., & Tao, T. (2006). Stable signal recovery from incomplete and inaccurate measurements. Communications on pure and applied mathematics, 59(8), 1207-1223.
- Candse, E. J. (2006, August). Compressive sampling. In Proceedings of the international congress of mathematicians (Vol. 3, pp. 1433-1452).
- Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on information theory, 52(4), 1289-1306.
- Castro, R., Haupt, J., & Nowak, R. (2006). Compressed sensing vs. active learning. In IEEE International Conference on Acoustics, Speech and Signal Processing, Proceedings. (Vol. 3, pp. III-III). IEEE.
- Elad, M., & Bruckstein, A. M. (2002). A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Transactions on Information Theory, 48(9), 2558-2567.
- Donoho, D. L., & Stark, P. B. (1989). Uncertainty principles and signal recovery. SIAM Journal on Applied Mathematics, 49(3), 906-931.
TutorialsEdit
SoftwareEdit
- pycompsense - Python
- pyCSalgos - Python
- Sparco - MATLAB
- SparseLab - MATLAB
- SparseMRI - MATLAB
- SPArse Modeling Software (SPAMS) - Python and R
- KL1p - C++
See alsoEdit
Other ResourcesEdit
- Learning Compressed Sensing - Nuit Blanche blog
- Compressive Sensing - Reddit
- Compressive Sensing on Google+ - online community
- Compressive Sensing Resources - Rice
- Compressive Sensing: The Big Picture
- Compressive Sensing:A New Framework for Imaging
- Uncertainty Principle in Quantum Physics and Signal Processing - blog post
- A Brief Introduction to Compressed Sensing with Scikit-Learn - blog post
- Compressive sensing: tomography reconstruction with L1 prior (Lasso) - blog post
- Compressed Sensing in Python - blog post
- Image reconstruction using compressed sensing - StackExchange