Adaptive unsupervised deep learning denoising for medical imaging with unbiased estimation and Hessian-based regularization

Abstract

This paper introduces an adaptive, unsupervised deep learning model for denoising Gaussian noise in Magnetic Resonance Imaging (MRI) images. The model is combined with Deep Image Prior (DIP) and Stein's Unbiased Risk Estimate (SURE) and incorporates a regularization term based on the Frobenius norm of the Hessian matrix. Leveraging the SURE criterion, the observed noisy image is used as the network input, significantly accelerating convergence speed and achieving more than a tenfold improvement over DIP. The real-time, adaptive adjustment of regularization intensity, driven by SURE, ensures robust performance across varying noise levels while effectively balancing the preservation of fine image details with noise elimination. The Hessian-based regularization captures second-order variations, promoting smoothness while preserving critical structural details. Experimental results demonstrate the model's superiority, with an average 8.7% increase in PSNR and a 10.1% increase in SSIM compared to DIP achieved. Furthermore, by the 25th iteration, the SSIM value of the proposed method had already surpassed the peak value reached by DIP at the 700th iteration and by DIP variants at the 2000th iteration. These advantages, coupled with the adaptive regularization strength adjustment, demonstrate the model's potential to enhance diagnostic accuracy and efficiency in medical applications.