Sparse recovery with general frame via general-dual-based analysis Dantzig selector

This paper considers recovery of signals that are sparse or approximately sparse in terms of a general frame from undersampled data corrupted with additive noise. We show that the properly constrained l(1)-analysis, called general-dual-based analysis Dantzig selector, stably recovers a signal which is nearly sparse in terms of a general dual frame provided that the measurement matrix satisfies a restricted isometry property adapted to the general frame. As a special case, we consider the Gaussian noise.