I am an Assistant Professor of Electrical Engineering at Harvard University, directing the Signals, Information, and Networks Group (SING) at the School of Engineering and Applied Sciences. At SING, we investigate the following two lines of research:

1. Sampling, representations, and inference for dynamics on networks;
2. Sampling and inference for spatiotemporal single-photon imaging.

Research at SING is supported by NSF, Mass General Hospital, the MIT Lincoln Scholar Program, the Croucher Foundation, and Agilent Technologies.

# Randomized algorithms for large-scale image filtering

January 8, 2014

We propose a randomized version of the non-local means (NLM) algorithm for large-scale image filtering. When applied to denoising images using an external database containing ten billion patches, our algorithm returns a randomized solution that is within 0.2 dB of the full NLM solution while reducing the runtime by three orders of magnitude. See our paper for more details.

# New paper: Sparse representation à la Prony

October 23, 2013

We consider the classical problem of finding the sparse representation of a signal in a pair of bases. When both bases are orthogonal, it is well-known that the sparse representation is unique when the sparsity $K$ of the signal satisfies $K<1/\mu(\mD)$, where $\mu(\mD)$ is the mutual coherence of the dictionary. Furthermore, the sparse representation can be obtained in polynomial time by Basis Pursuit (BP), when $K<0.91/\mu(\mD)$. Therefore, there is a gap between the unicity condition and the one required to use the polynomial-complexity BP formulation.

# Paper in Foundation and Trends in Signal Processing

September 30, 2012

The long overview paper, Multidimensional Filter Banks and Multiscale Geometric Representations, provides a systematic development of the theory and constructions of multidimensional filter banks and sparse representations that can efficiently capture directional and geometric features of multidimensional signals.

# Welcome to new group member

August 30, 2012
Welcome to Ariana Minot, who joined my group in August. Ariana received her Bachelor of Science degree in Physics and Mathematics from Duke University in 2010. She is a Ph.D. student in Harvard's applied math program, and a recipient of a three-year NSF Graduate Research Fellowship.

# Imaging by One-Bit Pixels

June 5, 2011

Before the advent of digital image sensors, photography, for the most part of its history, used film to record light information. In the paper Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics, we study a new digital image sensor that is reminiscent of photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity.