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I have had the opportunity to work on a number of interesting problems through the course of my PhD research. For my thesis work, I have used ideas from manifold learning and machine learning to solve optimization problems in order to recover MR images from highly undersampled measurements. In addition, I have also worked on deep learning and have explored different architectures during my internship and through personal projects and collaborations.
Accelerating free-breathing Cardiac MRI
Accelerating free-breathing Cardiac MRI
Magnetic Resonance Imaging (MRI) is a slow imaging modality, imposing restrictions on the achievable spatial and temporal resolution in dynamic imaging of organs such as the heart. The clinical state-of-the-art technique in cardiac MRI is to ask the patient to perform breath-holds, which is challenging in many patient populations. I have developed an acquisition scheme and a reconstruction algorithm (SToRM) to enable recovery of the images from highly undersampled measurements in the free-breathing mode. The proposed scan is as long as a typical breath-held scan and produces images of comparable quality.
Clustering Data with Missing Entries
Clustering Data with Missing Entries
The problem of finding patterns in datasets in the presence of a large number of missing entries is a challenging one. I developed an algorithm to find clusters in data when a few features might be unknown for every data point. The developed method uses a non-convex fusion penalty to group together similar data points. Our theoretical guarantees provide a bound for the probability of success of the algorithm based on the characteristics of the data and the number of missing entries.
Deep Learning for Magnetic Resonance Fingerprinting
Deep Learning for Magnetic Resonance Fingerprinting
I spent Summer 2016 as a Research Intern at Siemens Healthineers, Princeton, working on MR Fingerprinting (MRF). MRF is a recently developed and extremely popular and powerful technique to estimate the T1 and T2 parameter maps of different organs from a short MRI scan. My project involved improving the efficiency of MRF by replacing the traditional dictionary matching step with a CNN based approach for faster and more accurate parameter estimation.
I am currently extending this work with the aim of further increasing the parameter estimation accuracy.
Recovery of Points on the Zero-level set of a Band-limited Function
Recovery of Points on the Zero-level set of a Band-limited Function
I worked on the problem of denoising points lying near the zero-level set of a band-limited function. This model can represent a wide variety of closed and open shapes. I derived theoretical guarantees for the number of points that are required to be sampled to uniquely recover the surface, and developed an algorithm for the recovery of the points from corrupted measurements.
Learning a Language Model from a Joke Corpus
Learning a Language Model from a Joke Corpus
I have been working on a project to train a deep LSTM network to tell jokes! I initially came across this problem on Open AI 's list of fun problems in Deep Learning. My network isn't that funny yet, but I am working on it. I am using this dataset of around 200,000 jokes from Kaggle.
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