medical image teams

Abstract: We study the recovery of forward and reverse quadratic optimal-transport maps from unpaired samples in high dimensions. We introduce a bidirectional neural framework in which the learned maps induce forward and backward displacement interpolants, while the training objective combines bidirectional quadratic action, discriminator-restricted Jensen-Shannon endpoint objectives, and two-sided cycle consistency. The construction requires neither precomputed sample pairings nor an explicit convex-potential parameterization. For absolutely continuous probability measures supported on a compact convex set, and under the stated generator-approximation, discriminator-richness, and minimizer-attainment conditions, we prove a population recovery theorem: for every prescribed accuracy, the sum of the corresponding \(L^2\) errors between any global minimizer and the forward and reverse quadratic Brenier maps is below that accuracy, provided the discriminator level is sufficiently large and the annealing action weight becomes sufficiently small. Moreover, the cycle loss is bounded above by \(λW_2^2(μ_0,μ_1)\). Complementary results quantify approximate invertibility and show that exact endpoint Jensen-Shannon divergence and cycle consistency control missing target mass and many-to-one map collapse, respectively. Experiments on Swiss roll, MNIST, CelebA, single-cell perturbation data, and chest X-ray images evaluate endpoint fidelity, transport cost, inverse consistency, and the geometry of the induced interpolations.

Abstract: Lung cancer causes more deaths than any other malignancy, and low-dose CT screening is the main pathway to early diagnosis. That pathway hinges on the smallest lesions, yet nodules below six millimeters remain hard to detect, because most methods treat a nodule as a generic object and ignore the imaging physics behind its appearance. We show that this appearance is highly regular. Intensity peaks at the geometric center of a nodule and decays radially in a Gaussian pattern, and a fit to 18,218 annotated lesions from three public benchmarks yields a mean radial coefficient of determination above 0.86 in every dataset and size stratum. A square convolution samples both axes uniformly and is mismatched to this radial signal, most severely for small nodules. Guided by this evidence, we propose GRIPNet (Gaussian Radial Intensity Prior Network), a detector in which every module maps to a measurable property of the intensity distribution. Pinwheel convolutions decompose radial gradients, a dual-frequency module separates boundary detail from structural context, dilated masked attention matches the decay extent, and an adaptive loss reweights samples by conspicuity. GRIPNet raises mAP@0.5 to 95.3, 91.6 and 97.9 percent on KanserSet, LUNA16 and Lung-PET-CT-Dx while sharpening high-IoU localization at real-time speed.