Learning Data Triage: Linear Decoding Works for Compressive MRI

ABSTRACT 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. Index Terms-- Compressive sampling, magnetic resonance imaging (MRI), learning, least squares estimation, submodular minimization 1. INTRODUCTION The standard theory of compressive sampling (CS) considers recovering an unknown deterministic signal with certain known structure, and designing sampling and recovery schemes based on the known structure [11].