On Recovery of Sparse Signals Via \ell Minimization

• Published in: IEEE transactions on information theory Vol. 55; no. 7; pp. 3388 - 3397
• Main Authors: Cai, T.T., Guangwu Xu, Jun Zhang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Compressed sensing; Dantzig selector ell _{1} minimization; Equations; Gaussian noise; Information processing; Least squares methods; Linear regression; Minimization methods; Noise measurement; Optimization techniques; restricted isometry property; Signaling; sparse recovery; sparsity; Statistics; Vectors

This paper considers constrained lscr 1 minimization methods in a unified framework for the recovery of high-dimensional sparse signals in three settings: noiseless, bounded error, and Gaussian noise. Both lscr 1 minimization with an lscr infin constraint (Dantzig selector) and lscr 1 minimization u...