Linearized Analysis of Noise and Resolution for DL Based Image Generation

Deep-learning (DL) based CT image generation methods are often evaluated using RMSE and SSIM. By contrast, conventional model-based image reconstruction (MBIR) methods are often evaluated using image properties such as resolution, noise, bias. Calculating such image properties requires time consuming Monte Carlo (MC) simulations. For MBIR, linearized analysis using first order Taylor expansion has been developed to characterize noise and resolution without MC simulations. This inspired us to investigate if linearization can be applied to DL networks to enable efficient characterization of resolution and noise. We used FBPConvNet as an example DL network and performed extensive numerical evaluations, including both computer simulations and real CT data. Our results showed that network linearization works well under normal exposure settings. For such applications, linearization can characterize image noise and resolutions without running MC simulations. We provide with this work the computational tools to implement network linearization. The efficiency and ease of implementation of network linearization can hopefully popularize the physics-related image quality measures for DL applications. Our methodology is general; it allows flexible compositions of DL nonlinear modules and linear operators such as filtered-backprojection (FBP). For the latter, we develop a generic method for computing the covariance images that is needed for network linearization.