AWFSD: Accelerated Wirtinger Flow with Score-based Diffusion Image Prior for Poisson-Gaussian Holographic Phase Retrieval

Phase retrieval (PR) is an essential problem in a number of coherent imaging systems. This work aims at resolving the holographic phase retrieval problem in real world scenarios where the measurements are corrupted by a mixture of Poisson and Gaussian (PG) noise that stems from optical imaging systems. To solve this problem, we develop a novel algorithm based on Accelerated Wirtinger Flow that uses Score-based Diffusion models as the generative prior (AWFSD). In particular, we frame the PR problem as an optimization task that involves both a data fidelity term and a regularization term. We derive the gradient of the PG log-likelihood function along with its corresponding Lipschitz constant, ensuring a more accurate data consistency term for practical measurements. We introduce a generative prior as part of our regularization approach by using a score-based diffusion model to capture (the gradient of) the image prior distribution. We provide theoretical analysis that establishes a critical-point convergence guarantee for the proposed AWFSD algorithm. Our simulation experiments demonstrate that: 1) The proposed algorithm based on the PG likelihood model enhances reconstruction compared to that solely based on either Gaussian or Poisson likelihood. 2) The proposed AWFSD algorithm produces reconstructions with higher image quality both qualitatively and quantitatively, and is more robust to variations in noise levels when compared with state-of-the-art methods for phase retrieval.

Integrating cross-modality hallucinated MRI with CT to aid mediastinal lung tumor segmentation

Lung tumors, especially those located close to or surrounded by soft tissues like the mediastinum, are difficult to segment due to the low soft tissue contrast on computed tomography images. Magnetic resonance images contain superior soft-tissue contrast information that can be leveraged if both modalities were available for training. Therefore, we developed a cross-modality educed learning approach where MR information that is educed from CT is used to hallucinate MRI and improve CT segmentation. Our approach, called cross-modality educed deep learning segmentation (CMEDL) combines CT and pseudo MR produced from CT by aligning their features to obtain segmentation on CT. Features computed in the last two layers of parallelly trained CT and MR segmentation networks are aligned. We implemented this approach on U-net and dense fully convolutional networks (dense-FCN). Our networks were trained on unrelated cohorts from open-source the Cancer Imaging Archive CT images (N=377), an internal archive T2-weighted MR (N=81), and evaluated using separate validation (N=304) and testing (N=333) CT-delineated tumors. Our approach using both networks were significantly more accurate (U-net $P <0.001$; denseFCN $P <0.001$) than CT-only networks and achieved an accuracy (Dice similarity coefficient) of 0.71$\pm$0.15 (U-net), 0.74$\pm$0.12 (denseFCN) on validation and 0.72$\pm$0.14 (U-net), 0.73$\pm$0.12 (denseFCN) on the testing sets. Our novel approach demonstrated that educing cross-modality information through learned priors enhances CT segmentation performance