Transform Learning for Magnetic Resonance Image Reconstruction: From Model-Based Learning to Building Neural Networks

Magnetic resonance imaging (MRI) is widely used in clinical practice, but it has been traditionally limited by its slow data acquisition. Recent advances in compressed sensing (CS) techniques for MRI reduce acquisition time while maintaining high image quality. Whereas classical CS assumes the images are sparse in known analytical dictionaries or transform domains, methods using learned image models for reconstruction have become popular. The model could be prelearned from data sets or learned simultaneously with the reconstruction, i.e., blind CS (BCS). Besides the well-known synthesis dictionary model, recent advances in transform learning (TL) provide an efficient alternative framework for sparse modeling in MRI. TL-based methods enjoy numerous advantages, including exact sparse-coding, transform-update, and clustering solutions; cheap computation; and convergence guarantees; and they provide high-quality results in MRI compared to popular competing methods. This article reviews some recent works in MRI reconstruction from limited data, with a focus on the recent TL-based methods. We present a unified framework for incorporating various TL-based models and discuss the connections between TL and convolutional or filter-bank models and corresponding multilayer extensions, with connections to deep learning. Finally, we discuss recent trends in MRI, open problems, and future directions for the field.