Fourier Domain Robust Denoising Decomposition and Adaptive Patch MRI Reconstruction

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Science

Background:

• Magnetic Resonance Imaging (MRI) reconstruction often relies on k-space data, but noise and undersampling present significant challenges.
• Existing unsupervised methods show promise but struggle with noise interference and domain differences in low undersampled MRI data.
• Robust dictionary learning for MRI reconstruction is often computationally expensive due to nonconvexity.

Purpose of the Study:

• To propose a novel method for Fourier domain robust denoising decomposition and adaptive patch MRI reconstruction (DDAPR).
• To address the limitations of existing methods by considering noise interference and domain differences in low undersampled MRI data.
• To develop a computationally efficient and robust MRI reconstruction technique.

Main Methods:

• DDAPR employs a two-step optimization process: a low-rank and sparse denoising reconstruction model (LSDRM) followed by a robust dictionary learning reconstruction model (RDLRM).
• LSDRM utilizes proximal gradient methods with singular value decomposition and soft thresholding for optimization across different domains.
• RDLRM introduces a low-rank and sparse penalty adaptive patch dictionary, approximating undersampled data with a sparse rank-one matrix, optimized via block coordinate descent (BCD).

Main Results:

• Extensive numerical experiments demonstrate that DDAPR outperforms previous compressed sensing and deep learning-based methods in image reconstruction quality.
• The proposed LSDRM effectively handles noise and domain differences, improving reconstruction from low undersampled MRI data.
• The RDLRM component provides robust adaptive patch learning, contributing to superior reconstruction accuracy.

Conclusions:

• DDAPR offers a significant advancement in MRI reconstruction, particularly for noisy and highly undersampled datasets.
• The method's two-step optimization strategy effectively tackles the complexities of denoising and adaptive patch learning in MRI.
• DDAPR presents a promising alternative to existing reconstruction techniques, offering improved performance and robustness.