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Data representation using optimal transport, 2025, preprint
Linear optimal transport subspaces for point set classification (JMIV. 2025). Paper
Illumination invariant face recognition using optimal transport, (Pat. Rec 2025). Paper
End-to-end signal classification in signed cumulative distribution transform space (TPAMI 2024). Paper
The signed cumulative distribution transform (SCDT). 2022 AIMS FOD Paper
Mathematical representations of functions and data, such as signals and images, play a central role in mathematics, science, and engineering. Classical examples include the Fourier and wavelet transforms, which provide linear and multiresolution representations that facilitate the analysis of differential equations, shift-invariant systems, and transient phenomena. With the advent of modern machine learning, the need for nonlinear representation techniques has become increasingly important. We have recently introduced new function/signal/image representation techniques based on the mathematics of optimal transport. Like the Fourier representation method, the new techniques comprise a set of invertible mathematical function/measure transforms. They have the mathematical properties that can be used to simplify data classes for AI/ML problems. The new framework can render data classes convex in transform space (see side Figure) and thus significantly facilitate the solution of a classification problem. We are investigating the application of this new function representation technique to modeling the solutions of partial differential equations, machine learning, inverse problems, structural health monitoring, computer vision, and a variety of additional applications.
Dynamical systems and optimal transport
Dynamical systems and optimal transport
In collaboration with colleagues at the Office of Naval Research, Naval Research Laboratory and other colleagues we're developing new theory and algorithms for solving data science problems emanating from dynamical systems. Specifically we are using transport-based representation theory for modeling wave propagation and related physical processes, and using these models to solve important problems in science and engineering. Specifically, we are utilizing transport theory for designing new algorithms for reduced order modeling, dynamical mode decomposition and new general methods for representing solutions of dynamical system PDES. Using these methods we are also designing next generation detection and estimation solutions for a variety of applications as structural health monitoring, survaillance, target recognition, communications and other applications.
Data-driven identification of parametric governing equations of dynamical systems using the signed cumulative distribution transform, 2024, paper
Transport wave propagation model for for partially coherent polarization-gradient vector beams. JOSA A, 2023. paper
Transport-based pattern recognition versus deep neural networks in underwater OAM communications. JOSA A, 2021/ paper
Parametric Signal Estimation Using the Cumulative Distribution Transform. IEEE TSP 2020. paper
Digital microscopy and computational diagnosis
Digital microscopy and computational diagnosis
Transport-based morphometry of nuclear structure in cancer, 2025 paper
Effects of COVID‐19 vaccinations on platelets, Cytometry A 2023 paper
Single-cell profiling reveals high levels of circulating platelet aggregates in patients with COVID-19, Nat. Comm. 2021 paper
Nuclear chromatin changes in melanoma. paper
Digital microscopy is helping revolutionize cancer research, diagnosis, and treatment. Quantitative image analysis methods can help extract objective quantitative information from large quantities of cells. This information can in turn be used to build predictive models to describe effects of perturbations (e.g. drugs), as well as for aiding diagnosis and prognosis from histology/cytology images. We are working closely with pathologists, physicians and scientists accross multiple institutions in the US and beyond to transform digital pathology images into scientifically interpretable information to help pathology imaging into a cheap, reliable and quantitative discipline and help improve patient diagnosis, prognosis and outcomes.
Transport-based morphometry for medical imaging
Transport-based morphometry for medical imaging
Image-based models of structure-function relationships can greatly facilitate our understanding of living systems. Based on a new signal transformation being developed (see here for more information) our group is developing a new approach for quantifying the structure (i.e. shape, texture information) of biological forms seamlessly from image data. The new approach is ideally suited for forms which are associated with transport processes, though it can be used more generally. It has been used to model structure-function relationships and build predictive models of cancer from nuclear structure, knee osteoarthritis from MRI data, reaction time in concussed patients from diffusion MRI data, and others.
Predictive modeling of hematoma expansion from non-contrast computed tomography in spontaneous intracerebral hemorrhage patients, eLife, 2025 paper
Discovering the gene-brain-behavior link in autism via generative machine learning, 2025, Science advances, 2024, paper
Cardiorespiratory fitness in reducing brain tissue loss caused by ageing, 2021 paper .
Pre-symptomatic early detection of osteoarthritis from knee MRIs. PNAS, 2020. paper
Discovery and visualization of structural biomarkers from MRI using transport-based morphometry, Neuroimage 2018. preprint
Annually in the US, roughly 1 in every 330 households reported a home fire. There is a house fire every 98 seconds and a death once every three hours. Even though over 7 billion in property damage happens every year, 30% of smoke alarms do not work when tested, and smoke alarms are not sounded in 47% of house fires. We are working on algorithms to render any camera enabled smart device (e.g. cell phone, tablet, computer, nanny cam, etc.) into a working smoke detector thus delivering constant, ubiquitous smoke detection and monitoring.
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