Control of variance and bias in CT image processing with variational training of deep neural networks

Optimization of CT image quality typically involves balancing noise and bias. In filtered back-projection, this trade-off is controlled by the particular filter and cutoff frequency. In penalized-likelihood iterative reconstruction, the penalty weight serves the same function. Deep neural networks typically do not provide this tuneable control over output image properties. Models are often trained to minimize 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. In this work, 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 includes separate weighting parameters to control the relative importance of noise or bias reduction. Moreover, we show that tuning these weights enables targeted penalization of specific image features (e.g. spatial frequencies). To evaluate our method, we present a simulation study using digital anthropormorphic phantoms, physical simulation of non-ideal CT data, and image formation with various algorithms. We show that WCB offers a greater degree of control over trade-offs between variance and bias whereas MSE has only one 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 stimulus detectability. Our results demonstrate the potential for this new capability to control the image properties of DNN outputs and optimize image quality for the task-specific applications.