Abhinav V. Sambasivan — Research Projects

Fundamental parameter estimation limits for plenoptic imaging systems

Advisor: Professor Jarvis Haupt, UMN-Twin Cities,
Collaborator: Dr. Richard Paxman, MDA Systems

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 model

Advisor: 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 systems

Advisors: 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 quadrotors

Advisor: 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 robots

Advisor: 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 projects

These are some of the course projects I have done at UMN.

  • Identifying Salient Features in MR images using Outlier Pursuit
    In this project, we considered the problem of identifying salient features (like tumors or clots) in MR images using an outlier pursuit approach. We consider a model where the data (MR image) can be written as a sum of low rank and column sparse matrices, and developed an ADMM based solver to recover the locations of the sparse column outliers. This algorithm is shown to correctly recover the locations of the outliers, and also converge linearly. (Report)

  • Image Classification using Machine Learning techniques
    Built and trained an image classifier which extracts significant features in the image and distinguishes between two different genus of bees (bumble bee, and the honey bee). Various ML algorithms including kernel SVM, sparse logistic regression and random forests were used to develop and train the classifier. (Report)

  • Stock Price Prediction using Adaptive Learning Techniques
    Implemented and tested various adaptive models to predict the stock prices of a particular stock (in this case Yahoo's). Various error metrics including mean squared error, mean absolute error and the direction of sign change (whether the stock value is expected to increase or decrease) were analyzed. The different adaptive architectures studied and implemented include: Multiple Auto-regressive model, Linear combiner architecture, Volterra series based non-linear model and a Neural Network based Multi-Layer Perceptron (MLP) architecture.

  • Image Deblurring with Wiener Deconvolution
    The Wiener Deconvolution technique was used to recover images corrupted with distortions and motion blurs. This includes images from Hubble telescopes with lens aberrations and images of fireworks taken with significant motion blurring.

  • Handwritten Digit Recognition using Artificial Neural Networks
    Trained a simple 3 layer ANN for the recognition of handwritten digits. The images were passed through a dimensionality reduction block (I used PCA, to identify the significant features) prior to classification by the Neural Net to speed up the process.

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

  • A. V. Sambasivan, R. G. Paxman, and J. D. Haupt, “Computer Graphics meets Estimation Theory: Computing Parameter Estimation Lower Bounds for Non-Line-Of-Sight Plenoptic Imaging Systems”. Asilomar Conference on Signals, Systems, and Computers, November 2019. (PDF)

  • M. Soltani, S. Jain, A. V. Sambasivan, and Chinmay Hegde, “Learning Structured Signals Using GANs with Applications in Denoising and Demixing”. Asilomar Conference on Signals, Systems, and Computers, November 2019. (PDF)

  • M. Soltani, S. Jain, A. V. Sambasivan, “Unsupervised Demixing of Structured Signals from Their Superposition Using GANs”. Deep Generative Models for Highly Structured Data, ICLR workshop, May 2019. (PDF, ArXiv )

  • A. V. Sambasivan and J. D. Haupt, “Minimax Lower Bounds for Noisy Matrix Completion under Sparse Factor Models”. IEEE Transactions on Information Theory, vol. 64, no. 5, pp. 3274-3285, February 2018. (ArXiv)

  • A. V. Sambasivan, L. DelaBarre, E. S. Ebbini, J. T. Vaughan, and A. Gopinath, “RF Shimming for High Field MRI using Multi-channel Receive-Signals”. ISMRM - 24th Annual Meeting, May 2016.

Talks and Presentations

  • Computer Graphics meets Estimation Theory: Computing Parameter Estimation Lower Bounds for Non-Line-Of-Sight Plenoptic Imaging Systems.
    SIAM conference on Imaging Science, Bologna-Italy, June 2018.

  • Digital Beamforming for MRI Systems.
    10th Biennial 2015 Minnesota Workshop on High and Ultra-High Field Imaging, Centre for Magnetic Resonance and Research, University of Minnesota, Twin Cities, October 2015 (Poster).