A Note on Stability and Instance Optimality in Compressed Sensing
In this note, it is proved that every -sparse signal vector can be recovered stably from the measurement vector via minimization as soon as the restricted isometry constant of the measurement matrix is smaller than . Note that our results contain the case of noisy data, therefore previous known results in the literature are extent and improved. Also we obtain the results on the stability and instance optimality for some random measurement matrices.
S. Zhang and P. X. Ye, "A Note on Stability and Instance Optimality in Compressed Sensing", Applied Mechanics and Materials, Vols. 130-134, pp. 4194-4197, 2012