chinmay hegde

We are in the throes of a 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.

union-of-subspace models for signals/images

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

model-based compressive sensing

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

manifold models for signal/image ensembles

image synthesis and modeling

Explores the use of optical flow in learning certain classes of image manifolds. Applications include image synthesis, parameter estimation, and charting.
Paper: framework, applications

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

adapted sampling

Develops a convex method for designing sub-Nyquist measurement kernels adapted to data from low-dimensional manifolds, and/or adapted to a specified signal processing task (note the distinction from adaptive sampling, also referred to as active sensing).
Paper: algorithm, applications to imaging.

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.

nonparametric models for images

image upsampling

Develops a highly efficient algorithm for the upsampling of edges and textures in natural photos. Our algorithm can crisply upscale a 200x200 image by a factor of 4x in less than a minute.
Paper: layer-based upsampling