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We study verifiable sufficient conditions and computable performance boundsfor sparse recovery algorithms such as the Basis Pursuit, the Dantzig selectorand the Lasso estimator, in terms of a newly defined family of quality measuresfor the measurement matrices. With high probability, the developed measures forsubgaussian random matrices are bounded away from zero as long as the number ofmeasurements is reasonably large. Comparing to the restricted isotropicconstant based performance analysis, the arguments in this paper are much moreconcise and the obtained bounds are tighter. Numerical experiments arepresented to illustrate our theoretical results.

Sparse recovery based on q-ratio constrained minimal singular values