I had the opportunity to study Compressed Sensing for my Undergraduate thesis under K.V.S Hari and Chandra Sekhar Seelamantula at the Indian Institute of Science.
The Shannon-Nyquist theorem has been the cornerstone of Information Theory for over 80 years. It states that a signal must be sampled at least at twice the rate of its maximum frequency content in order to reconstruct it without loss. In accordance with this theory, all modern digital systems acquire data at this rate and then compress it to save space and bandwidth. Recently, a new sampling/sensing paradigm called Compressed Sensing was developed which states that certain signals with specific structures can be sampled at a rate much lower than that stipulated by the Nyquist theorem, and these ‘under-sampled’ signals can be recovered satisfactorily using linear programming techniques.
The main aim of this project was to study Compressed Sensing (CS) and its reconstruction algorithms, and apply this knowledge to real world signals like Optical Coherence Tomography (OCT) and images. The project is roughly divided into three parts. In the first part, a few CS algorithms are implemented in Matlab and tested on artificial data. In the second, CS algorithms are implemented on OCT and image data. The last part consists of results of CS algorithms applied on OCT data using a special ‘sparsifying’ basis and its comparison with different algorithms.
You can find a copy of the report here.
There are, however, some results that were obtained after the report was submitted for review. Read on…
Extending previous work in the field, we used a windowed cosine function as a sparsifying basis, and applied and compared various ‘greedy’ algorithms to recover the image, pictured in the following montage of an onion peel.
In summary, we discarded 80% of the data in an OCT scan randomly, and reconstructed it with insignificant error and less noise than the current standard reconstruction technique. It could result in cheaper, faster, and more efficient OCT scans in the future.
Tags: 2012, DSP, Image Processing, Indian Institute of Science, Matlab, OCT