Abhinav V. Sambasivan — Research ProjectsFundamental parameter estimation limits for plenoptic imaging systemsAdvisor: Professor Jarvis Haupt, UMN-Twin Cities, The plenoptic function (or the light-field) is 5D function which describes the amount of light flowing in every direction through every point in space. Light-fields are information-rich and it is possible to discern a lot more information about some scene of interest using plenoptic imaging systems over conventional imaging tools such as simple cameras. Hence it is of interest to quantify the fundamental limits of plenoptic imaging systems in noisy and noise-free scenarios. In this project, we develop a framework to obtain lower bounds for parameter estimation using computational tools, such as Ray-tracing softwares. We consider extensions to the classical Cramer-Rao lower bounds which are very restrictive in their applicability, to a broader class of lower bounds called the Barankin bounds. These bounds are more amenable to our settings where obtaining partial derivative of the log-likelihood function w.r.t the parameter(s) of interest can be hard or impossible to obtain. Minimax analysis for matrix completion under sparse factor modelAdvisor: Professor Jarvis Haupt, UMN-Twin Cities Matrix Completion is the problem of finding the missing elements of a partially sampled (or filled) matrix. Without additional information this problem is ill-posed as the missing entries can be arbitrary. But if the unknown matrix is assumed to have some intrinsic structure like low-rank or sparsity, then the problem of completing the matrix becomes interesting. Such completion problems have found widespread applications and uses (e.g the Netflix challenge). In particular, we consider the problem of noisy matrix completion where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy (where we examine several noise models). Our focus here has been to establish minimax lower bounds for the best achievable error in the setting described above. (See Publications section for more details) Digital beamforming algorithm for MRI systemsAdvisors: Professor Anand Gopinath, and Professor Emad Ebbini, UMN-Twin Cities At high fields (especially 7T and beyond), magnetic field inhomogeneities severely affect the imaging capabilities of the current MRI machines. The focus of this project is to develop clever schemes for Phased-Array MRI systems which overcome the effects of such inhomogeneities and produce image-reconstructions with uniform contrast. We use a beamforming based approach which utilizes the transmit and receive element directivity patterns of the various RF elements. At each image pixel, a spatially-varying weighting vector is computed for combining the complex-valued image data from different receiving elements. This approach employs a regularized spatial inverse filter derived from the transmit-receive directivities to equalize the array gain at each pixel. The objective of this project is to enable clinicians to select and highlight certain regions of interest in the MRI images without the need for further scans. Stability analysis of quadrotorsAdvisor: Professor V. Sankaranarayanan, NIT-Tiruchirappalli Worked on building a Stable Quadrotor which can hover autonomously in a steady state position. Accelerometers and Gyroscopes are extensively used for the purpose sensing the inertial state of robots these days. However both these sensors give highly noisy (with different types of corruptions) readings when used directly. I designed and implemented a digital filter (called the complementary filter) to correct the erroneous sensor data. This filter was able to rectify the high frequency noise from the accelerometer and the DC bias from the gyro sensor simultaneously and it had low latency which is essential for the dynamic state estimation of quadrotors. Thus we used it as an alternative to more complicated Kalman Filters. Indoor positioning of robotsAdvisor: Professor K.V.S Hari, Indian Institute of Sciences, Bangalore Built prototypes of unmanned motorized vehicles which navigate autonomously to act as first responders during times of emergency (like fires or gas leaks). These robots were fit with an IMU (inertial sensors) which was used for Indoor Positioning, cameras and a DSP board to transmit a live video stream wirelessly. We developed a system which gives the exact location of these robots and a simultaneous video stream from each of the robots. Selected Course projectsThese are some of the course projects I have done at UMN.
During my Bachelor’s, I worked on several interesting and small robotic projects including building line-follower robots, four-legged walking robot, and self balancing robot (a.k.a Mobile Inverted Pendulum unit). Here is a link to a short video compilation of these projects. Publications
Talks and Presentations
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