[Paper Review] A Theoretically Guaranteed Deep Optimization Framework for Robust Compressive Sensing MRI

Risheng Liu, Yuxi Zhang+3 more|arXiv (Cornell University)|Nov 9, 2018

Advanced MRI Techniques and Applications1 references4 citations

TL;DR

This paper proposes a theoretically guaranteed deep optimization framework for robust compressive sensing MRI by integrating designed numerical solvers with data-driven architectures, ensuring convergence via an optimal condition checking mechanism and explicitly modeling Rician noise for real-world robustness. The method achieves state-of-the-art reconstruction accuracy, efficiency, and noise resilience in MRI recovery from highly undersampled k-space data.

ABSTRACT

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.

Motivation & Objective

• To address the lack of theoretical convergence guarantees in deep learning-based CS-MRI methods that use experience-driven architectures.
• To improve robustness to real-world Rician noise in MRI acquisition by explicitly modeling noise distributions within the optimization framework.
• To unify model-based numerical solvers with data-driven deep architectures for enhanced reconstruction performance.
• To establish a convergence-proof deep optimization scheme for nonconvex sparse recovery in CS-MRI using the Kurdyka-Łojasiewicz (KŁ) property and optimal condition checking.

Proposed method

• Integrates a designed numerical solver (based on proximal gradient method) with a learnable deep architecture within an unrolled optimization framework.
• Employs an optimal condition checking mechanism to ensure theoretical convergence of the deep optimization scheme.
• Models Rician noise explicitly in the data fidelity term to improve robustness to real-world MRI acquisition noise.
• Uses the Kurdyka-Łojasiewicz (KŁ) inequality to prove sequence convergence of the iterative algorithm, establishing theoretical guarantees.
• Applies a nonconvex ℓp regularization (p ∈ (0,1)) for sparsity promotion in the sparse coding domain.
• Unrolls the optimization iterations into a deep network with learnable parameters, while preserving convergence via analytical constraints.

Experimental results

Research questions

• RQ1 Can a deep optimization framework for CS-MRI be designed with theoretical convergence guarantees?
• RQ2 How can Rician noise in real MRI acquisitions be explicitly modeled within a deep CS-MRI framework to improve robustness?
• RQ3 Can the integration of model-based solvers and data-driven architectures outperform existing state-of-the-art methods in reconstruction quality and efficiency?
• RQ4 What is the impact of using nonconvex ℓp regularization (p ∈ (0,1)) on reconstruction accuracy and convergence in deep CS-MRI?

Key findings

• The proposed framework achieves theoretical convergence of the deep optimization scheme through optimal condition checking and the KŁ property, resolving a key limitation of prior unrolled networks.
• Explicit modeling of Rician noise leads to significantly improved robustness to real-world noise in MRI data, outperforming methods that ignore or approximate noise.
• The method outperforms existing state-of-the-art CS-MRI techniques in both reconstruction accuracy and computational efficiency, especially at high undersampling ratios.
• Extensive experiments on multiple sampling patterns (Cartesian, radial, Gaussian) confirm consistent superiority across different k-space sampling schemes.
• The convergence analysis proves that the sequence of iterates is Cauchy and thus convergent, validating the stability of the proposed deep optimization framework.