  The standard approach to compressive sampling considers recovering an unknown
deterministic signal with certain known structure, and designing the
sub-sampling pattern and recovery algorithm based on the known structure. This
approach requires looking for a good representation that reveals the signal
structure, and solving a non-smooth convex minimization problem (e.g., basis
pursuit). In this paper, another approach is considered: We learn a good
sub-sampling pattern based on available training signals, without knowing the
signal structure in advance, and reconstruct an accordingly sub-sampled signal
by computationally much cheaper linear reconstruction. We provide a theoretical
guarantee on the recovery error, and show via experiments on real-world MRI
data the effectiveness of the proposed compressive MRI scheme.
