J. Webster Stayman

Jacopo Teneggi, Matthew Tivnan, J. Webster Stayman et al.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

Yijie Yuan, Grace J. Gang, J. Webster Stayman

The restoration of images affected by blur and noise has been widely studied and has broad potential for applications including in medical imaging modalities like computed tomography (CT). Although the blur and noise in CT images can be attributed to a variety of system factors, these image properties can often be modeled and predicted accurately and used in classical restoration approaches for deconvolution and denoising. In classical approaches, simultaneous deconvolution and denoising can be challenging and often represent competing goals. Recently, deep learning approaches have demonstrated the potential to enhance image quality beyond classic limits; however, most deep learning models attempt a blind restoration problem and base their restoration on image inputs alone without direct knowledge of the image noise and blur properties. In this work, we present a method that leverages both degraded image inputs and a characterization of the system blur and noise to combine modeling and deep learning approaches. Different methods to integrate these auxiliary inputs are presented. Namely, an input-variant and a weight-variant approach wherein the auxiliary inputs are incorporated as a parameter vector before and after the convolutional block, respectively, allowing easy integration into any CNN architecture. The proposed model shows superior performance compared to baseline models lacking auxiliary inputs. Evaluations are based on the average Peak Signal-to-Noise Ratio (PSNR), selected examples of good and poor performance for varying approaches, and an input space analysis to assess the effect of different noise and blur on performance. Results demonstrate the efficacy of providing a deep learning model with auxiliary inputs, representing system blur and noise characteristics, to enhance the performance of the model in image restoration tasks.

Xiao Jiang, Grace J. Gang, J. Webster Stayman

In this work, we introduce a new deep learning approach based on diffusion posterior sampling (DPS) to perform material decomposition from spectral CT measurements. This approach combines sophisticated prior knowledge from unsupervised training with a rigorous physical model of the measurements. A faster and more stable variant is proposed that uses a jumpstarted process to reduce the number of time steps required in the reverse process and a gradient approximation to reduce the computational cost. Performance is investigated for two spectral CT systems: dual-kVp and dual-layer detector CT. On both systems, DPS achieves high Structure Similarity Index Metric Measure(SSIM) with only 10% of iterations as used in the model-based material decomposition(MBMD). Jumpstarted DPS (JSDPS) further reduces computational time by over 85% and achieves the highest accuracy, the lowest uncertainty, and the lowest computational costs compared to classic DPS and MBMD. The results demonstrate the potential of JSDPS for providing relatively fast and accurate material decomposition based on spectral CT data.