Rank Estimation of Low Rank Matrices using Compressive Sensing

Basic Information

Project Title: Rank Estimation of Low Rank Matrices using Compressive Sensing
Name: Adit Akarsh
Project: BTP
Semester(s): Autumn 2022-23
Guide: Ajit Rajwade, Nikhil Karamchandani

Abstract

A large amount of real-world data is high-dimensional, for example, images and videos. However, the data in different dimensions is highly correlated, and using techniques like principal component analysis (PCA), the data can be compressed to a lower dimension without significant loss in information. However, these methods require either manual tuning of hyperparameters or the rank to be known. Thus, we worked on rank estimation methods for large, low-rank matrices using compressive measurements (that reduce the size of the matrix we work with).

Any courses you completed relevant to the project

CS 754: Advanced Image Processing, CS 663: Digital Image Processing

Describe your experience on the project

I liked the contents of both the image processing courses I completed, so I wanted to work on something in this domain. The work built up almost entirely on the Compressive Sensing and Low Rank Matrices segments of CS 754, and was a mixture of theoretical and programming components for conducting experiments.

The workload was about 4-6 hours per week, mostly consisting of reading and understanding previous literature, modifying the ideas used and simulating them using MATLAB/Python.

There was not any publication based on the work done.

I worked on extending the results to noisy (approximately low-rank) matrices in the following semester.

Describe your experience with the guide

The guide’s level of involvement seemed to drop about a month into the semester (when he started teaching a course). He thought about and discussed the project only during our meetings. We had meetings one 1-hour meeting every week throughout the semester. The guide was approachable for questions on Teams/email but he mostly addressed them only during meetings. The evaluation included a report, a presentation with him and 2 EE professors (co-guide and examiner) as the evaluators.

Any advice for anyone considering a project under the same guide? Any other professors working in similar fields?

If working with a non-EE professor, talk to an EE guide beforehand and try to meet him occasionally in the semester. I am not aware of any other professor working on compressive sensing/image processing without ML in the institute.