A constrained bregman framework for unsupervised convolutional denoising of multi-channel x-ray ct data
Deep learning (DL) approaches to image denoising have advanced real-world performance in one of the most thoroughly studied areas of digital signal processing. Keys to the success of DL are data-driven approximation of an underlying signal model and non-linear domain mapping. By contrast, "classic"denoising approaches rely on prior assumptions about the structure of data and noise and generally penalize deviations through convex optimization. Despite these apparent differences, denoising with CNNs can be viewed as an extension of older sparse coding models, and even state-of-the-art DL models commonly employ cost terms like mean-squared-error and total variation. In this work, we adapt the split Bregman optimization method (SBM) for use with CNN-based regularizers. We show how the operator splitting of the SBM lends itself to splitting cost terms for CNN-based denoising, simplifying the selection of regularization hyperparameters and the hybridization of classic and DL-specific regularizers (bilateral TV, patch rank, discriminator loss). Furthermore, we demonstrate a simple, data-driven method to rebalance cost terms during network training, while limiting the potential to "invent"features. Using preclinical photon-counting micro-CT data of the mouse heart, our proposed framework performs 2D denoising of the time (PSNR, 27.7; SSIM, 0.62) and energy (PSNR, 35.0; SSIM, 0.81) dimensions which compares favorably with both 3D, multi-channel iterative reconstruction (reference) and the BM3D denoising algorithm (time: PSNR, 26.6; SSIM, 0.58. energy: PSNR, 27.2; SSIM, 0.76). The time and energy networks evaluate in under 2 minutes each vs. ∼1-2 hours for our iterative reconstructions using similar hardware.
