SpiNet: A deep neural network for Schatten p-norm regularized medical image reconstruction

Area of Science:

• Medical Imaging
• Deep Learning
• Image Reconstruction

Background:

• Model-based deep learning architectures for inverse problems typically enforce L1 or L2 norms.
• Existing methods have limitations in flexibility and performance with increasing undersampling rates.

Purpose of the Study:

• To propose SpiNet, a generic deep learning model for medical image reconstruction.
• To enable the enforcement of any Schatten p-norm (0 < p ≤ 2) regularization.
• To allow the parameter 'p' to be learned or fixed based on the specific problem.

Main Methods:

• Developed a model-based deep learning architecture combining a denoiser and a data consistency solver.
• Implemented a Majorization-Minimization algorithm to enforce any p-norm (0 < p ≤ 2).
• Tested SpiNet for magnetic resonance (MR) image reconstruction from undersampled k-space data, comparing it with MoDL across various undersampling rates (R=2x to 20x).

Main Results:

• SpiNet demonstrated superior performance over MoDL across all tested undersampling rates, showing higher PSNR and SSIM, and lower NRMSE.
• At higher undersampling rates (≥6x), SpiNet achieved significant improvements, up to 4 dB in PSNR and 0.5 points in SSIM.
• At lower undersampling rates (2x, 4x), performance was comparable as the learned 'p' value approached 2.

Conclusions:

• SpiNet offers a versatile framework for medical image reconstruction using generalized Schatten p-norm regularization.
• The model achieves superior performance compared to existing methods, particularly at high undersampling rates.
• SpiNet's ability to automatically learn the optimal Schatten p-norm value from data is a key advantage.