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

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.