research
Research
PROFESSIONAL BACKGROUND:
· Post-doctoral Associate with Singapore-MIT Alliance Research and Technology Centre since Sept 2014- May 2016.
· Worked as a Research Fellow at the National University of Singapore since August 2010-July 2014.
· Worked as Scientist in DRDO (Electronics and Radar Development Establishment), India for 3 yrs.
MY PROFESSIONAL EXPERIENCES
Introduction
Mankind has always been very inquisitive. We want to know about the things we do not know, understand the things we do not understand, predict the outcomes of events, and find out the contents of the regions we cannot access. This quest for the unknown has made us look into the sky, dig deeper into the earth, hear to the sounds of nature and predict danger, cut open the dead bodies to understand anatomy, and a lot of other things. With the advances in sciences and technology, our quest for knowledge has extended to include our desire to control the things which were beyond our control earlier. We want to find if we have competitors out there in space or are we awaiting a visit from a deadly comet; find the reservoirs of resources inside the earth and use them for mankind; rescue people from an impending or existing dangerous situation; diagnose tumors and remove them surgically or treat them; bore a very fine thread of one material into another, design nanowires, and further revolutionize the already fast-paced digital world.
In other words, we want to collect the data we can, and then interpret the data to find more about the underlying cause. Such problems are generally called the inverse problems. We also want to learn about the various physical phenomena in mathematical terms and use them to design better techniques to produce and control the desired effects. These problems are generally called model estimation/characterization and design problems.
The inverse problems, model estimation problems, and design problems are my primary research interests. Within the wide scope of such problems, I am particularly interested in the problems related to electromagnetics, photon transport, and biomedical research fields. I am also interested in design, evaluation and applications of materials exhibiting special electromagnetic properties like anisotropy, metamaterials, plasma medium, etc. My doctoral thesis concentrated on electromagnetic inverse problems. In particular, the concepts of operator theory were used for solving electromagnetic and biomedical imaging problems. The thesis also deals with electromagnetic inverse problems for anisotropic and uniaxial materials. In this research statement, I shall first introduce my previous and current research works. This shall be followed by my research goals for near future.
Doctoral Research (Link to my thesis)
Detecting small scatterers
Multiple Signal Classification (MUSIC) was developed by the signal processing community for radar signal processing and estimation of the direction of arrival of aircrafts. It was adopted for inverse scattering problems in acoustics by the group of A. J. Devaney. My work applied MUSIC for the case of two dimensional electromagnetic case. The multistatic response (MSR) matrix (corresponding to a MIMO system) is the fundamental operator used for detecting the scatterers. For the transverse magnetic (TM) waves, the orthogonality of the null space of the MSR matrix with a test line source implies the presence of a scatterer. On the other hand, for the transverse electric (TE) waves, the orthogonality of the null space of the MSR matrix with a test dipole source implies the presence of a scatterer. An example of imaging small scatterers using MUSIC in 20 dB SNR is shown below:
(a) MUSIC - TM case (b) MUSIC - TE case (x-dipole) (c) MUSIC - TE case (y-dipole)
Imaging large scatterers
Linear sampling method (LSM) is used for finding the scatterer support (shape and location of the scatterers) of large scatterers. My work presented a physics based interpretation of the linear sampling method. Instead of using the complete non-linear scattering model, it uses a simple linear model that approximates the induced current on the scatterers such that the radiation from the induced current is similar to a fundamental source. In addition, we propose a multipoles based linear sampling method (MLSM) that is more effective than the original LSM in imaging large scatterers. Some examples are shown below.
(a) Scatterer Profile (b) Original LSM (c) MLSM (N=1)
Detecting small anisotropic scatterers
For detecting anisotropic scatterers and uniaxial scatterers, it is essential to choose an optimal direction of the test dipole used in MUSIC. We proposed a modification of MUSIC that is capable of choosing the optimal test direction analytically and non-iteratively. An example of detection of three scatterers in 20 dB SNR is shown below:
(a) MUSIC (x-dipole) (b) MUSIC (y-dipole) (c) modified MUSIC
Reconstructing large anisotropic scatterers
Large anisotropic scatterers can be reconstructed using the subspace based optimization method (SOM). If the optic axis is known, the numerical complexity of applying SOM is the same for isotropic lossless scatterers as well as lossy anisotropic scatterers, though the number of unknowns in the latter case is four times the former case. Further, reconstructed profiles of anisotropic scatterers show significant directional behaviour. Some portions of the scatterers are better reconstructed than the others along an optic axis. See below for an example.
(1) Real part of the relative permiitivity along the first optic axis
(2) Real part of the relative permiitivity along the second optic axis
(3) Imaginary part of the relative permiitivity along the first optic axis
(4) Imaginary part of the relative permiitivity along the second optic axis
(a) Actual permittivity profile
(b) Permittivity profile reconstructed by SOM after 20 iterations
We see that the horizontal portions are reconstructed well in (b1,b3) and vertical portions are reconstructed well in (b2,b4). The directionality is explained by the nature of the induced currents. See the picture below.
Magnitude of the sum of all induced currents due to all the incident waves is plotted here. (a) current components along the first optic axis (b) current components along the second optic axis.
We see that the currents along the vertical portions of the scatterer are weaker in (1) above and currents along the horizontal portions of the scatterers are weaker in (2) above. Therefore, reconstructing the vertical portions along the first optic axis is difficult. Similar conclusion holds for the second optic axis as well.
A modification of SOM for reconstructing anisotropic scatterers of unknown optic axis was also presented.
Practical inverse problems
Diffusion Optical Tomography for breat tissue imaging
Diffusion optical tomography is a popular biomedical imaging technique. Photon density waves are used to illuminate the biological tissue and the photon density waves scatterers by the tissue are measured at various detectors. The measured scattered photon densities are used to image the biological tissue. The physical model of the scattering and absorption of photons is given by the equation of radiative transfer (ERT), also called the Boltzmann photon transport model. This model considers vectorial photon density waves and is a highly non-linear model.