Control of Variance and Bias in CT Image Processing with Variational Training of Deep Neural Networks

Tunable neural networks for CT image formation

Optimization of CT image quality typically involves balancing variance and bias. In traditional filtered back-projection, this trade-off is controlled by the filter cutoff frequency. In model-based iterative reconstruction, the regularization strength parameter often serves the same function. Deep neural networks (DNNs) typically do not provide this tunable control over output image properties. Models are often trained to minimize the expected mean squared error, which penalizes both variance and bias in image outputs but does not offer any control over the trade-off between the two. We propose a method for controlling the output image properties of neural networks with a new loss function called weighted covariance and bias (WCB). Our proposed method uses multiple noise realizations of the input images during training to allow for separate weighting matrices for the variance and bias penalty terms. Moreover, we show that tuning these weights enables targeted penalization of specific image features with spatial frequency domain penalties. To evaluate our method, we present a simulation study using digital anthropomorphic phantoms, physical simulation of CT measurements, and image formation with various algorithms. We show that the WCB loss function offers a greater degree of control over trade-offs between variance and bias, whereas mean-squared error provides only one specific image quality configuration. We also show that WCB can be used to control specific image properties including variance, bias, spatial resolution, and the noise correlation of neural network outputs. Finally, we present a method to optimize the proposed weights for a spiculated lung nodule shape discrimination task. Our results demonstrate this new image quality can control the image properties of DNN outputs and optimize image quality for task-specific performance.

Task-Driven CT Image Quality Optimization for Low-Contrast Lesion Detectability with Tunable Neural Networks

Low-contrast lesions are difficult to detect in noisy low-dose CT images. Improving CT image quality for this detection task has the potential to improve diagnostic accuracy and patient outcomes. In this work, we use tunable neural networks for CT image restoration with a hyperparameter to control the variance/bias tradeoff. We use clinical images from a super-high-resolution normal-dose CT scan to synthesize low-contrast low-dose CT images for supervised training of deep learning CT reconstruction models. Those models are trained using with multiple noise realizations so that variance and bias can be penalized separately. We use a training loss function with one hyperparameter called the denoising level, which controls the variance/bias tradeoff. Finally, we evaluate the CT image quality to find the optimal denoising level for low-contrast lesion detectability. We evaluate performance using a shallow neural network model classification model to represent a suboptimal image observer. Our results indicate that the optimal networks for low-contrast lesion detectability are those that prioritize bias reduction rather than mean-squared error, which demonstrates the potential clinical benefit of our proposed tunable neural networks.