Tomography is a non-invasive technique to view the internal structure of an object, by irradiating it with powerful electromagnetic rays. In comparison to the more common 2D X-ray imaging for, say, fractures, tomography involves rays sent from multiple directions. This technique finds applications in fields as varied as medicine (for diagnosis), manufacturing (to detect cracks in products), material science (to study the interaction of materials over time), and geophysics (to identify fossil fuels in the earth’s crust), among various other disciplines.
The amount of X-rays absorbed by the object depends on the material properties of the object. Rays that aren’t absorbed are then measured after propagating through the object. The process of recovering the 3D structure of the entire object from these measurements is referred to as ‘reconstruction’. The quality of reconstruction depends on the number of measurements acquired. The more the measurements, the more accurate the reconstructed volume representative of the true internal structure of the object.
Figure 1. Illustration of the tomography process for an object. For clarity, this image shows one direction: rays are being sent from top to bottom. In reality, multiple directions are employed.
However, acquiring a large number of measurements for, say, a patient, implies exposure to higher levels of the X-ray radiation, which is harmful in the long run. It can also be expensive, and may require the patient to be immobile. In order to overcome these shortcomings, current research aims to build algorithms that help reconstruct the 3D object volume reasonably well with very few measurements.
The classical Nyquist-Shannon sampling theorem asserts the need to sample data at a uniform rate of at least twice the highest frequency contained in the data. For long, this remained the guideline for computing the minimum number of measurements needed. In 2006, a new theory, ‘Compressive Sensing’, emerged. This guaranteed robust reconstruction with measurements far fewer than the Nyquist rate. Compressive Sensing exploits the fact that most naturally occurring data are usually sparse under mathematical transforms such as the Discrete Cosine Transform, wavelets, or some other unique basis. Over the last decade, the focus has been on improving the efficiency of reconstruction by using domain knowledge of the data together with Compressive Sensing routines.
It is in this context that my research fits in. It aims to drastically reduce the number of needed measurements using two ideas:
- suitable pre-processing
- use of prior information of the family of objects scanned, perhaps over time
Specifically, the problems I deal with include: optimal grouping of 2D slice (cross-section of 3D volume) measurements, registration of 2D slices in the Radon and Fourier domains, and effective use of prior information within the Compressive Sensing framework. My work is particularly useful in scenarios wherein a person undergoing a long-term treatment needs to get a scan at regular intervals. In such a case, the information from earlier scans can be effectively used to reduce the X-ray dosage in later scans.
Figure 2 . Overview of the updated reconstruction process in Preeti Gopal’s research
I also intend to work on developing and selecting the best direct reconstruction technique that would serve as a good initialization for iterative reconstruction routines. In the next couple of years, I aim to further explore applications of computational image analysis.
We, graduate research scholars of the IITB-Monash Research Academy, study for a dually-badged PhD from IIT Bombay and Monash University, spending time at both institutions to enrich our research experience. The Academy is a collaboration between India and Australia that endeavours to strengthen relationships between the two countries. According to its CEO, Prof Murali Sastry, “The IITB-Monash Research Academy was conceived as a unique model for how two leading, globally focussed academic organisations can come together in the spirit of collaboration to deliver solutions and outcomes to grand challenge research questions facing industry and society.”
He was bang on target. It is fascinating to learn how interdisciplinary healthcare is. Physicians dictate what needs to be seen for diagnosis and treatment; physicists and material scientists work on building the hardware; and finally, computer scientists’ work on developing optimal algorithms to compute the desired entity from as few resources as possible. My research is on the algorithms front and aims to reduce exposure to X-ray radiation due to a scan.
Research scholar: Preeti Gopal , IITB-Monash Research Academy
Project title: Improving tomographic reconstruction from sparse measurements
Supervisors: Dr. Ajit Rajwade, Dr. Sharat Chandran, Dr. Imants Svalbe
Contact details: firstname.lastname@example.org
This story was written by Preeti Gopal. Copyright IITB-Monash Research Academy.