Reference for RIP, RE, & other conditions used in theory for the Lasso

Statistics for High-dimensional Data, Buhlmann & van de Geer, 2011 (You can download the pdf for free from the U of C library, try this link.) See Chapter 6 = "Theory for the Lasso".

Links for Restricted Isometry Property (RIP):

RIP for basis pursuit, original paper: Decoding for Linear Programming, Candes & Tao 2004.

RIP for basis pursuit overview: The Restricted Isometry Property and Its Implications for Compressed Sensing, Candes, 2008.

RIP for orthogonal matching pursuit: Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property, Davenport & Wakin, 2010

Proving that a random matrix satisfies RIP: A Simple Proof of the Restricted Isometry Property for Random Matrices, Baraniuk et al, 2008.

RIP of a submatrix of a Fourier matrix: On the Restricted Isometry of Deterministically Subsampled Fourier Matrices, Haupt et al, 2010.

Links for Restricted Eigenvalues (RE):

RE for Lasso (see Thm 6.2): Simultaneous Analysis of Lasso and Dantzig Selector, Bickel et al, 2009

Proving that a random matrix satisfies RE: Restricted Eigenvalue Properties for Correlated Gaussian Designs, Raskutti et al, 2010.