Task-based Regularization in Penalized Least-Squares for Binary Signal Detection Tasks in Medical Image Denoising

TL;DR

The paper addresses the loss of task-relevant information in medical image denoising that can arise from conventional penalties or loss functions aligned with generic image quality metrics. It proposes a task-based regularization term linked to the log-likelihood of a linear observer's test statistic under Gaussian noise, embedded in a penalized least-squares framework with a TV penalty. The method yields per-image optimization with no requirement for ground-truth data and demonstrates improved signal detectability (ROC AUC) on MVNLumpy and binary texture backgrounds compared to baseline TV-denoising and CNN denoisers. This task-aware denoising approach offers a principled path to preserve clinically relevant information and motivates future extension to non-linear observers.

Abstract

Image denoising algorithms have been extensively investigated for medical imaging. To perform image denoising, penalized least-squares (PLS) problems can be designed and solved, in which the penalty term encodes prior knowledge of the object being imaged. Sparsity-promoting penalties, such as total variation (TV), have been a popular choice for regularizing image denoising problems. However, such hand-crafted penalties may not be able to preserve task-relevant information in measured image data and can lead to oversmoothed image appearances and patchy artifacts that degrade signal detectability. Supervised learning methods that employ convolutional neural networks (CNNs) have emerged as a popular approach to denoising medical images. However, studies have shown that CNNs trained with loss functions based on traditional image quality measures can lead to a loss of task-relevant information in images. Some previous works have investigated task-based loss functions that employ model observers for training the CNN denoising models. However, such training processes typically require a large number of noisy and ground-truth (noise-free or low-noise) image data pairs. In this work, we propose a task-based regularization strategy for use with PLS in medical image denoising. The proposed task-based regularization is associated with the likelihood of linear test statistics of noisy images for Gaussian noise models. The proposed method does not require ground-truth image data and solves an individual optimization problem for denoising each image. Computer-simulation studies are conducted that consider a multivariate-normally distributed (MVN) lumpy background and a binary texture background. It is demonstrated that the proposed regularization strategy can effectively improve signal detectability in denoised images.

Figures (5)

• Figure 1: Examples of the generated MVNLumpy background images.
• Figure 2: Examples of the generated binary texture background images.
• Figure 3: (a) The ROC curves produced by denoised images using different $\gamma$ values and original noisy images on the MVNLumpy object model. (b) Evaluation results on the binary texture model: the AUC values corresponding to denoised images with different total variation regularization parameters $\beta$ and different task-based regularization parameters $\gamma$, and the AUC values corresponding to the original noisy data and CNN denoised images are plotted.
• Figure 4: (a) ground-truth signal-present image; (b) noisy signal-present image; (c) denoised image using DnCNN; (d) - (j) denoised images using proposed method under different $\gamma$ values with $\alpha=1$ and $\beta=0.14$.
• Figure 5: Difference maps between denoised images produced by the task-based PLS-TV method ($\gamma>0$) and the traditional PLS-TV method ($\gamma=0$).