Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices
Oliver James. Article: Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices. International Conference on Current Trends in Advanced Computing (ICCTAC-2015) ICCTAC 2015(2):1-5, May 2015. Full text available. BibTeX
@article{key:article,
author = {Oliver James},
title = {Article: Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices},
journal = {International Conference on Current Trends in Advanced Computing (ICCTAC-2015)},
year = {2015},
volume = {ICCTAC 2015},
number = {2},
pages = {1-5},
month = {May},
note = {Full text available}
}
Abstract
In this paper, we introduce a new framework for interpreting the existing theoretical stability results of sparse signal recovery algorithms in practical terms. Our framework is built on the theory of constrained minimal singular values of Gaussian sensing matrices. Adopting our framework, we study the stability of two algorithms, namely LASSO and Dantzig selector. We demonstrate that for a given stability parameter (noise sensitivity), there exits a minimum undersampling ratio above which the recovery algorithms are guaranteed to be stable.
References
- Barry C. Arnold, N. Balakrishnan, and H. N. Nagaraja. A First Course in Order Statistics. SIAM, Philadelphia.
- Emmanuel J. Candes. The restricted isometry property and its implications for compressed sensing. C. R. Acad. Sci. Paris, Ser. I.
- Emmanuel J. Candes and Terence Tao. Decoding by linear programming. IEEE Transactions on Information Theory.
- Enrique Castillo, Ali S. Hadi, N. Balakrishnan, and Jose M. Sarabia. Extreme Value and Related Models with Applications in Engineering and Science. John Wiley and Sons, New York.
- L. Canto E Castro. Uniform rates of convergence in extremevalue theory: Normal and gamma models. Annales de la Facult des sciences de l'Universit de Clermont, Srie Probabilits et applications.
- Paul Embrechts, Claudia Kluppelberg, and Thomas Mikosch. Modeling Extremal Events for Insurance and Finance. Springer Verlag, New York.
- I. S. Gradshteyn and I. M. Ryzhik. Table of Integrals, Series, and Products. Academics Press, San Diego.
- A. K. Gupta and D. K. Nagar. Matrix Variate Distributions. Chapman and Hall, Florida.
- Hwan-Chol Jang, Chang-Hyeong Yoon, Eui-Heon Chung, Won-Shik Choi, and Heung-No Lee. Speckle suppression via sparse representation for wide-field imaging through turbid media. Optics Express.
- Gongguo Tang and Arye Nehorai. Performance analysis of sparse recovery based on constrained minimal singular values. IEEE Transactions on Signal Processing.
- Brendt Wohlberg. Noise sensitivity of sparse signal representations: Reconstruction error bounds for the inverse problem. IEEE Transactions on Signal Processing.
- Hui Zhang and Lizhi Cheng. On the constrained minimal singular values for sparse signal recovery. IEEE Signal Processing Letters.