A Theoretically Guaranteed Deep Optimization Framework for Robust Compressive Sensing MRI

Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging techniques available for clinical applications. However, the rather slow speed of MRI acquisitions limits the patient throughput and potential indi cations. Compressive Sensing (CS) has proven to be an efficient technique for accelerating MRI acquisition. The most widely used CS-MRI model, founded on the premise of reconstructing an image from an incompletely filled k-space, leads to an ill-posed inverse problem. In the past years, lots of efforts have been made to efficiently optimize the CS-MRI model. Inspired by deep learning techniques, some preliminary works have tried to incorporate deep architectures into CS-MRI process. Unfortunately, the convergence issues (due to the experience-based networks) and the robustness (i.e., lack real-world noise modeling) of these deeply trained optimization methods are still missing. In this work, we develop a new paradigm to integrate designed numerical solvers and the data-driven architectures for CS-MRI. By introducing an optimal condition checking mechanism, we can successfully prove the convergence of our established deep CS-MRI optimization scheme. Furthermore, we explicitly formulate the Rician noise distributions within our framework and obtain an extended CS-MRI network to handle the real-world nosies in the MRI process. Extensive experimental results verify that the proposed paradigm outperforms the existing state-of-the-art techniques both in reconstruction accuracy and efficiency as well as robustness to noises in real scene

Proximal Alternating Direction Network: A Globally Converged Deep Unrolling Framework

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent studies build deep structures by unrolling a particular optimization model that involves task information. Unfortunately, due to the dynamic nature of network parameters, their resultant deep propagation networks do \emph{not} possess the nice convergence property as the original optimization scheme does. This paper provides a novel proximal unrolling framework to establish deep models by integrating experimentally verified network architectures and rich cues of the tasks. More importantly, we \emph{prove in theory} that 1) the propagation generated by our unrolled deep model globally converges to a critical-point of a given variational energy, and 2) the proposed framework is still able to learn priors from training data to generate a convergent propagation even when task information is only partially available. Indeed, these theoretical results are the best we can ask for, unless stronger assumptions are enforced. Extensive experiments on various real-world applications verify the theoretical convergence and demonstrate the effectiveness of designed deep models

Spin-glass ground state in a triangular-lattice compound YbZnGaO4_4

We report on comprehensive results identifying the ground state of a triangular-lattice structured YbZnGaO$_4$ to be spin glass, including no long-range magnetic order, prominent broad excitation continua, and absence of magnetic thermal conductivity. More crucially, from the ultralow-temperature a.c. susceptibility measurements, we unambiguously observe frequency-dependent peaks around 0.1 K, indicating the spin-glass ground state. We suggest this conclusion to hold also for its sister compound YbMgGaO$_4$, which is confirmed by the observation of spin freezing at low temperatures. We consider disorder and frustration to be the main driving force for the spin-glass phase.Comment: Version as accepted to PR