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
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.