A. Ribeiro

M. Zargham, A. Ribeiro, A. Jadbabaie et al.

Dual descent methods are commonly used to solve network optimization problems because their implementation can be distributed through the network. However, their convergence rates are typically very slow. This paper introduces a family of dual descent algorithms that use approximate Newton directions to accelerate the convergence rate of conventional dual descent. These approximate directions can be computed using local information exchanges thereby retaining the benefits of distributed implementations. The approximate Newton directions are obtained through matrix splitting techniques and sparse Taylor approximations of the inverse Hessian.We show that, similarly to conventional Newton methods, the proposed algorithm exhibits superlinear convergence within a neighborhood of the optimal value. Numerical analysis corroborates that convergence times are between one to two orders of magnitude faster than existing distributed optimization methods. A connection with recent developments that use consensus iterations to compute approximate Newton directions is also presented.

A. Candito, A. Dragan, R. Holbrey et al.

Background: Apparent Diffusion Coefficient (ADC) values and Total Diffusion Volume (TDV) from Whole-body diffusion-weighted MRI (WB-DWI) are recognized cancer imaging biomarkers. However, manual disease delineation for ADC and TDV measurements is unfeasible in clinical practice, demanding automation. As a first step, we propose an algorithm to generate fast and reproducible probability maps of the skeleton, adjacent internal organs (liver, spleen, urinary bladder, and kidneys), and spinal canal. Methods: We developed an automated deep-learning pipeline based on a 3D patch-based Residual U-Net architecture that localises and delineates these anatomical structures on WB-DWI. The algorithm was trained using "soft labels" (non-binary segmentations) derived from a computationally intensive atlas-based approach. For training and validation, we employed a multi-centre WB-DWI dataset comprising 532 scans from patients with Advanced Prostate Cancer (APC) or Multiple Myeloma (MM), with testing on 45 patients. Results: Our weakly-supervised deep learning model achieved an average dice score of 0.67 for whole skeletal delineation, 0.76 when excluding ribcage, 0.83 for internal organs, and 0.86 for spinal canal, with average surface distances below 3mm. Relative median ADC differences between automated and manual full-body delineations were below 10%. The model was 12x faster than the atlas-based registration algorithm (25 sec vs. 5 min). Two experienced radiologists rated the model's outputs as either "good" or "excellent" on test scans, with inter-reader agreement from fair to substantial (Gwet's AC1 = 0.27-0.72). Conclusion: The model offers fast, reproducible probability maps for localising and delineating body regions on WB-DWI, potentially enabling non-invasive imaging biomarker quantification to support disease staging and treatment response assessment.