Convergent Complex Quasi-Newton Proximal Methods for Gradient-Driven Denoisers in Compressed Sensing MRI Reconstruction
Journal:
arXiv
Published Date:
May 7, 2025
Abstract
In compressed sensing (CS) MRI, model-based methods are pivotal to achieving
accurate reconstruction. One of the main challenges in model-based methods is
finding an effective prior to describe the statistical distribution of the
target image. Plug-and-Play (PnP) and REgularization by Denoising (RED) are two
general frameworks that use denoisers as the prior. While PnP/RED methods with
convolutional neural networks (CNNs) based denoisers outperform classical
hand-crafted priors in CS MRI, their convergence theory relies on assumptions
that do not hold for practical CNNs. The recently developed gradient-driven
denoisers offer a framework that bridges the gap between practical performance
and theoretical guarantees. However, the numerical solvers for the associated
minimization problem remain slow for CS MRI reconstruction. This paper proposes
a complex quasi-Newton proximal method that achieves faster convergence than
existing approaches. To address the complex domain in CS MRI, we propose a
modified Hessian estimation method that guarantees Hermitian positive
definiteness. Furthermore, we provide a rigorous convergence analysis of the
proposed method for nonconvex settings. Numerical experiments on both Cartesian
and non-Cartesian sampling trajectories demonstrate the effectiveness and
efficiency of our approach.
