Learning Data Triage: Linear Decoding Works for Compressive MRI

TL;DR

This paper proposes a data-driven approach to compressive MRI that learns sub-sampling patterns from training data and uses simple linear reconstruction, offering theoretical guarantees and practical effectiveness.

Contribution

It introduces a novel method for data-driven sub-sampling pattern learning in MRI, bypassing the need for explicit signal structure knowledge.

Findings

The learned sub-sampling pattern improves MRI reconstruction quality.

Linear decoding achieves competitive results with traditional methods.

Theoretical guarantees support the approach's reliability.

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.