Stability and Instance Optimality in Compressed Sensing with Regard to Some Measurement Matrices

In this paper, it is proved that every s-sparse signal vector can be recovered stably from the measurement vector y = Ax via l₁ minimization as soon as the 2s-th restricted isometry constant of the measurement matrix A is smaller than 3/(4+√6). While for the large values of s, the constant can be improved to 4/(6 + √6)Note that our results contain the case of noisy data, therefore previous known results in the literature are extent and improved. Then we obtain the results on the stability and instance optimality for some random measurement matrices. Our results show there is a large family of measurement matrices which are suitable for compressed sensing.