Block sparse recovery via mixed l2/l1 minimization

We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ2s < 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l2/l1-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali (in IEEE Trans. Inform. Theory 55: 5302–5316, 2009). We also give another sufficient condition on block RIP for such recovery method: δs < 0.307.

[1]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[2]  Rémi Gribonval,et al.  Restricted Isometry Constants Where $\ell ^{p}$ Sparse Recovery Can Fail for $0≪ p \leq 1$ , 2009, IEEE Transactions on Information Theory.

[3]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[4]  Yonina C. Eldar,et al.  Robust Recovery of Signals From a Structured Union of Subspaces , 2008, IEEE Transactions on Information Theory.

[5]  Song Li,et al.  New bounds on the restricted isometry constant δ2k , 2011 .

[6]  S. Foucart,et al.  Sparsest solutions of underdetermined linear systems via ℓq-minimization for 0 , 2009 .

[7]  Yonina C. Eldar,et al.  Block-Sparse Signals: Uncertainty Relations and Efficient Recovery , 2009, IEEE Transactions on Signal Processing.

[8]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[9]  Lie Wang,et al.  Shifting Inequality and Recovery of Sparse Signals , 2010, IEEE Transactions on Signal Processing.

[10]  Volkan Cevher,et al.  Model-Based Compressive Sensing , 2008, IEEE Transactions on Information Theory.

[11]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[12]  Lie Wang,et al.  New Bounds for Restricted Isometry Constants , 2009, IEEE Transactions on Information Theory.

[13]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .