[!TIP] We are currently looking for undergraduate, MS and PhD students (either incoming or already at UT) to join our lab!
- Prospective PhD students: Please e-mail me if you are interest in the BME or CSEM PhD program. Please include your CV, transcripts (unofficial copy is okay), and a brief description of your training and research interests. Please elaborate on your linear algebra, numerical methods & optimization background as well as programming skills.
- PhD students in BME and CSEM already in the program but still looking for a match: Please reach out!
- Undergraduate students in the Computational Science and Engineering Certificate: Yes! I can serve as the faculty mentor for your Scientific Computing Project
- Undergraduate students in BME: Please reach-out! Having taken BME 313L Intro to Numerical Methods is strongly encouraged for a successful research experience!
[!CAUTION] Please no unsolicited e-mail regarding serving as a Teaching Assistant (TA) for courses I offer. TA assignments are handled at the department level.
Some projects ideas for PhD and MS students
Dynamic contrast-enhanced (DCE) imaging – 4D/5D Image reconstruction methods for DCE photoacoustic tomography (PACT)
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Dynamic contrast-enhanced imaging of tumor perfusion plays a fundamental role in preclinical science to assess response to new treatments, such as anticancer drugs or radiotherapy. DCE PACT presents several advantages compared to other DCE imaging modalities, including fine spatial and temporal resolution, ease of detection of the arterial input function, and the fact of being free from ionizing radiation or potentially toxic contrast agents.
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In this project, we will use advanced numerical optimization method, including low-rank (non-negative) matrix factorization, tensor decomposition, etc to derive novel computationally and memory-efficient image reconstruction algorithms for large scale, multi-dimensional (three space dimensions, time, and optical wavelength) image reconstruction.
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Ideal background: Python, cuda, pytorch/jax, imaging science, numerical optimization, partial differential equations
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References: Lozenski 2022, Cam 2024, Lozenski 2024
Task-based assessment of image quality
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Medical images are taken for a specific clinical task (screening, diagnostics, monitoring). As such, physical measurements of image quality (such as mean square errors or structural similarity) do not always inform the clinical utility of the image. Task-based assessment of image quality, instead, use signal detection and numerical observer theory to measure the performance of a particular imaging system design or image reconstruction algorithm in performing a given clinically relevant task, e.g. detecting and/or segmenting a lesion, discriminating a benign lesion from a tumor.
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In this project, we will combine machine learning and image science to develop and assess conventional (model-based) and learned image reconstruction method in a principled manner by use of statistical signal detection theory and numerical observers.
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References: Lozenski 2024, Li 2024
Can you hear the shape of a tumor – Quantitative Photoacoustic Tomography
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In 1966 the Polish American mathematician Mark Kac asked the question: Can One Hear the Shape of a Drum? Using today’s medical imaging techniques, we can hear tumors! Photoacoustic tomography is an emerging medical imaging modality that uses light and sound to create 3D images of hemoglobin concentration and oxygen saturation within a target tissue. Since tumors consume a lot of energy to grow, regions of the image showing high hemoglobin concentration and low oxygen saturation may hint at the presence of tumor.
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In this project, we will use partial differential equations to model light and sound propagation, large-scale optimization methods to reconstruct images of hemoglobin concentration, machine learning to further refine those images.
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Ideal background: Python, pytorch/jax, numerical analysis, partial differential equations, and finite element methods.
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References: Park 2023, Scope Crafts 2024
Make each measurement count: smaller data, richer information
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Where should I measure? For how long? How often? Optimal design of experiments is an information-theoretic framework to guide how data are collected to maximize accuracy and reduce uncertainty in parameter estimation and image reconstruction problems.
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In this project, we will use numerical simulations and partial differential equations to model the measurement process, statistics and information theory to quantify the information gain using a particular set of measurements, and large-scale optimization to find the best design.
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Ideal background: Python, numerical optimization, linear algebra, partial differential equations.
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References: Scope Crafts 2024