chinmay hegde

We are in the throes of a digital data deluge. The vast amount of information generated by data sources positioned across the globe is poised to overwhelm current state-of-the-art data processing algorithms. Processing this information in any meaningful fashion is as difficult as searching for a tiny needle in a haystack.

Fortunately, some exciting recent developments in signal processing/machine learning can help counter this bleak possibility. The key insight is that despite its apparent high dimensionality, the aggregate data can instead be described using simple, low-dimensional geometric models. This geometric structure of the data not only enables efficient algorithms for extracting useful information from the data, but also lends itself to elegant analysis that characterizes the fundamental limits of these algorithms.

structured-sparse models for signals/images

model-based compressive sensing (model-CS)

Proposes a general framework for sub-Nyquist sampling and recovery sparse signals modeled as arising from a union of subspaces. Develops theory and algorithms that have been successfully used in a wide range of applications.
Papers: overall framework, more theory and fundamental limits, recovery of spike trains, blocky images, clustered spikes.

approximation-tolerant model-CS

Extends the model-CS framework to a far-richer class of structured-sparse models by leveraging a connection between compressive sensing and approximation algorithms. Applies this framework to the Constrained Earth Movers Distance (CEMD) model, particularly useful for modeling signal ensembles with correlated sparsity patterns.
Papers: overall framework, application to recovery of seismic data

sub-Nyquist sampling of bilinear models

Builds theory and algorithms for the sampling and recovery of signals that are the convolution of two sparse components.
Papers: overall framework, application to neuronal spikes, astronomical images

nonlinear models for signal/image ensembles

adapted sampling

Develops NuMax, a convex framework for designing near measurement kernels adapted to specific point-cloud or manifold data, and/or adapted to a specified signal processing task.
Papers: framework, algorithm and applications, applications to radar imaging, theoretical analysis.

multi-manifold signal recovery

Introduces and analyzes an algorithm for sampling and recovery of signals that are the linear sum of manifold-modeled components.
Paper: algorithm, geometric analysis

robust modeling of image manifolds

Leverages tools from computer vision to enable robust manifold learning algorithms for image collections gathered in the wild.

Papers: Optical flow-based manifold learning, keypoint-based manifold modeling.

compressive classification and parameter estimation

Enables methods for efficient multi-manifold data fusion for classification/parameter estimation. Relevant for networks of high-resolution static cameras observing a common scene.
Papers: overall framework, theoretical analysis of manifold learning, application to parameter estimation.