Research

Broadly my research interests lie in the domain of signal and image processing. I am particularly interested in the fields of compressed sensing and medical image processing and their applications to statistical inverse problems such as biomedical imaging using tomography and low-rank matrix recovery. The overall aim of my research has been to contribute to the field of biomedical imaging by helping visualize the structures of biological molecules in high-resolution which could be used for addressing fundamental questions in biomedicine. Visualizing molecular structures in incredible detail is decisive for both the basic understanding of life’s chemistry and for the development of pharmaceuticals.

Publications

† equal contribution

Competitions

  • IEEE Signal Processing Cup 2017 - Developed an algorithm to track the beats of a musical recording in real-time. Chunks of audio are obtained, and a corresponding sub-sampled function is designed such that it peaks on note onsets and sudden bursts in energy. Using this novelty curve, tempo for a section of audio is estimated and dynamically updated. We submitted this algorithm to the IEEE Signal Processing Cup 2017 and were ranked in the middle third (8-14) among 21 teams all over the world.

Bachelor’s Thesis

Research Projects

  • Graph Laplacian Tomography From Unknown Random Projections - Implemented a graph Laplacian-based algorithm to reconstruct an object from projections in unknown angles. The algorithm is shown to reconstruct the Shepp-Logan phantom from its noisy projections successfully. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.

  • Bayesian approach to cryo-EM structure determination - Spent the Summers of 2018 at EPFL as a research intern under Professor Victor Panaretos, the chair of mathematical statistics. Analyzed the algorithms of two standard reconstruction packages – RELION and CryoSPARC and implemented an accurate version of them for 2D structures. In the process, I developed an efficient yet accurate algorithm for the Radon transform and its corresponding back projection operation entirely in the Fourier domain. 

  • Tomographic reconstructions under unknown angles and shifts - Designed and implemented a way of recovering angles from a set of tomographic projections when the view-angles are completely unknown by exploiting the Helgason-Ludwig Consistency Conditions which relate the object moments to the projection moments. Improved the estimates by formulating the error function as a compressed sensing optimization problem taking advantage of the sparsity of signal in the DCT domain. Using techniques such as K-means clustering and PCA denoising I was able to achieve accurate reconstructions of the object.

Research Implementations

  • Robust Audio Watermarking - Implemented a method to embed a watermark into the maximal coefficient of discrete cosine transform of the moving average sequence. Empirical tests reveal that the algorithm is highly robust to common digital signal processing operations, including additive noise, sampling rate change, bit resolution transformation, MP3 compression, and random cropping, especially low-pass filtering.

  • Genre Identification - Identifying what genre a particular song belongs to has been a cakewalk for humans. Can we train the machines to do this job for us? With this motivation in mind, we used Machine Learning as a tool for implementing this task of genre identification. In this project, we have explored methods for exploratory data analysis, feature selection, hyperparameter optimization, and eventual implementation of several algorithms for classification.


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