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.

My current research interests focus on signal processing using approaches from statistical physics, and spatiotemporal single-photon imaging. In the past, I also worked on multidimensional sampling theory, multiscale geometrical representations, and image processing.

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

News

Randomized Kaczmarz algorithm: Annealed and quenched error exponents

October 22, 2014

The Kaczmarz method is a popular method for solving large-scale overdetermined systems of equations. Recently, Strohmer et al. proposed the randomized Kaczmarz algorithm, an improvement that guarantees exponential convergence to the solution. This has spurred much interest in the algorithm and its extensions. In our paper, we provide an exact formula for the mean squared error (MSE) in the value reconstructed by the algorithm.

Fast image reconstruction for spatiotemporal single photon imaging

October 1, 2014

Recent advances in materials, devices and fabrication technologies have spurred strong research interests in developing solid-state sensors that can detect individual photons in space and time. In our paper, we present an efficient algorithm to reconstruct images from the massive bit-streams generated by these sensors. 

Group member to join Purdue University

Group member to join Purdue University

May 22, 2014

Stanley Chan, a postdoc at SING, will join Purdue University this August as a tenure-track Assistant Professor of ECE and Statistics. Congratulations and best wishes, Stanley!

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.

Welcome to new group member

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

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.

ICASSP Best Student Paper Award

ICASSP Best Student Paper Award

March 21, 2011

The paper Can One Hear the Shape of a Room: The 2-D Polygonal Case was awarded the Best Student Paper Award at the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) in 2011. In a famous work, M. Kac asks the catchy question “Can you hear the shape of a drum?”. This problem is related to a question in astrophysics, and the answer is negative, meaning, different drum shapes can have the same resonant frequencies.