Imaging and Computing Group

Imaging and Computing Seminar — Spring 2011

Th 02/10, at 4:30pm, in room 32-G449 (Stata)

Arthur Szlam, CIMS, NYU.

Linear and piecewise linear data analysis

Abstract: Many data sets arising from signal processing or machine learning problems can be approximately modeled as a union of $K$ low dimensional linear sets. In this talk I will start by discussing the case $K=1$, which remains a surprisingly active area of research, despite more than a hundred years of history and a good understanding of the mathematics of the problem for many notions of "approximately" and "low". For larger values of $K$, although heuristic methods have proved succesful in applications, many basic mathematical and computational questions remain open. I will talk about some regimes where we have made progress, and then give some fun examples in less easy regimes where the math remains murky.
Mo 02/14, at 4:30pm, in room 54-517 (special day, room)

Russell Hewett, CS, UIUC.

Numerical Methods for Solar Tomography in the STEREO Era

Abstract: Despite its proximity, our collective understanding of the physical processes that drive the sun are incomplete. In particular, energetic and dynamic phenomena, such as active regions, solar flares, coronal mass ejections (CMEs), and solar wind, all of which contribute to geoeffective events collectively referred to as space weather, are not well understood. Knowledge of key physical parameters of the solar corona (or solar atmosphere), such as temperature and electron density, are critical to the understanding of the processes that drive coronal activity. This talk surveys new developments in key aspects of the mathematical and computational problems associated with the empirical estimation of these coronal parameters, including constrained methods for dynamic estimation, a phase field based level set method for tomography of CMEs from extremely limited points-of-view, and a scalable algorithm for constructing the tomographic projection matrices required for algebraic reconstruction methods.
Fr 02/18, at 4:30pm, in room 54-517 (special day, room)

Vincent Jugnon, Ecole normale superieure, Ulm, France.

Photo-acoustic imaging

Abstract: In photoacoustics, one triggers an acoustic wave with electromagnetic heating. The inverse problem is then to reconstruct the initial value of the wave equation from ultrasound boundary measurements. In an ideal frame, the problem has been thoroughly studied and inversion formulae involving spherical Radon transform are available. In this talk, I will address a number of non-idealities and the solutions we developped to deal with them. Modelling the EM heating is also of great importance in the photoacoustic problem. The optical coefficients can be linked to the initial pressure reconstructed from the acoustic inverse problem. I will finish by discussing our recent work on more classic wave imaging problems. I will develop an improvement of a topological derivative based algorithm for the Helmholtz equation ans compare it with classic approaches.
Th 02/24, at 4:30pm, in room 2-147

Lie Wang, Mathematics, MIT.

Square-root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming

Abstract: We propose a pivotal method for estimating high-dimensional sparse linear regression models. The method is a modification of Lasso, called square-root Lasso. The method neither relies on the knowledge of the standard deviation of the regression errors nor does it need to pre-estimate it. Despite not knowing the standard deviation, square-root Lasso achieves near-oracle performance, attaining the prediction norm convergence rate, and thus matching the performance of the Lasso. Moreover, we show that these results are valid for both Gaussian and non-Gaussian errors, under some mild moment restrictions, using moderate deviation theory.
Th 03/03, at 4:30pm, in room 2-147

Petros Boufounos, Mitsubishi Electric Research Laboratories, Cambridge.

Making sense of sensing

Abstract: The advent of Compressive Sensing (CS) has prompted a significant re-evaluation of our approach to signal acquisition and sensing. CS-inspired advances in computational signal acquisition enable us to achieve notable gains in sensing performance. The main components of the revisited approach are three: acquisition system models, signal models and cheap computation. After a brief introduction on the principles of computational signal acquisition, we will discuss acquisition system models and how they can accommodate quantization, saturation and unknown non-linear distortions. We will also present the components of a streaming CS framework and its application in high-speed video acquisition. The talk will conclude with some thoughts on the current challenges and the road ahead.

Bio: Petros Boufounos completed his undergraduate and graduate studies at MIT. He received the S.B. degree in Economics in 2000, the S.B. and M.Eng. degrees in Electrical Engineering and Computer Science (EECS) in 2002, and the Sc.D. degree in EECS in 2006. Since January 2009 he is with Mitsubishi Electric Research Laboratories (MERL) in Cambridge, MA and a complimentary visiting scholar at Rice University.

Between September 2006 and December 2008, Dr. Boufounos was with the Digital Signal Processing Group at Rice University doing research in the area of Compressive Sensing. Before that he was a postdoctoral associate in the MIT Digital Signal Processing Group. His primary research focus is Computational Signal Acquisition. He is broadly interested in signal processing, data representations and machine learning applied to signal processing. He is also looking into how computational sensing interacts with other fields that use sensing extensively, such as robotics and mechatronics. Dr. Boufounos has received the Ernst A. Guillemin Master Thesis Award for his work on DNA sequencing and the Harold E. Hazen Award for Teaching Excellence, both from the MIT EECS department. He has also been an MIT Presidential Fellow. Dr. Boufounos is a member of the IEEE, Sigma Xi, Eta Kappa Nu, and Phi Beta Kappa.
Th 03/31, at 4:30pm, in room 2-147

Thomas Hagstrom, Department of Mathematics, Southern Methodist University

Towards the Ultimate Solver for Wave Equations in the Time Domain

Abstract: Efficient time-domain solvers for wave propagation problems must include three crucial components:

i. Radiation boundary conditions which provide arbitrary accuracy at small cost (spectral convergence, weak dependence on the simulation time and wavelength)

ii. Algorithms for using the information at or near the boundary to directly propagate the solution to remote locations - avoid sampling the wave whenever possible.

iii. Reliable high-resolution volume discretizations applicable in complex geometry (i.e. on grids that can be generated efficiently) - we believe that high-resolution methods enabling accurate simulations with minimal dofs-per-wavelength are necessary to solve difficult 3+1-dimensional problems with the possibility of error control.

In this talk we will discuss recent developments in all three areas, including our own work on the construction of complete radiation boundary conditions (CRBCs), which are optimal local radiation conditions, as well as novel spectral elements based on Hermite interpolation.
Th 04/07, at 4:30pm, in room 54-517

Giovanni Meles, Geophysics, ETH, Zurich.

Recent Developments in GPR Full-waveform inversion

Abstract: Ground Penetrating Radar (GPR) full-waveform inversion is an advanced, high resolution, non-intrusive technique for mapping permittivity and conductivity distributions. GPR full-waveform inversion can be formulated as a non-linear least squares problem in which the misfit between observed and modeled data is minimized. The talk will focus on recent developments in GPR waveform imaging. Firstly, a general introduction to radar tomography will be given. Secondly, a newly developed time-domain/frequency-domain waveform imaging algorithm designed to tame the non-linearity problem associated with inverse scattering will be presented. Finally, an effective computational method of sensitivity patterns together with formal resolution and Jacobian spectral analyses for model appraisal will be discussed.
Th 04/21, at 4:30pm, in room 2-147

Cancelled (Simons lecture).
Th 04/28, at 4:30, in room 2-147

Yue Lu, SEAS, Harvard.

Gigapixel Binary Sensing: Image Acquisition Using One-Bit Poisson Statistics

Abstract: Before the advent of digital image sensors, photography, for the most part of its history, used film to record light information. In this talk, I will present 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.

To analyze its performance, we formulate the binary sensing scheme as a parameter estimation problem based on quantized Poisson statistics. We show that, with a single-photon quantization threshold and large oversampling factors, the Cramer-Rao lower bound of the estimation variance approaches that of an ideal unquantized sensor, that is, as if there were no quantization in the sensor measurements. Furthermore, this theoretical performance bound is shown to be asymptotically achievable by practical image reconstruction algorithms based on maximum likelihood estimators.

Numerical results on both synthetic data and images taken by a prototype sensor verify the theoretical analysis and the effectiveness of the proposed image reconstruction algorithm. They also demonstrate the benefit of using the new binary sensor in applications involving high dynamic range imaging.

Joint work with Feng Yang, Luciano Sbaiz and Martin Vetterli.
Mo 05/02, at 4:30pm, in room 2-136

Venkat Chandrasekaran, EECS, MIT.

The Convex Geometry of Linear Inverse Problems

Abstract: Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed. Examples of structured models include previously studied cases such as sparse signals and low-rank matrices, as well as others such as low-rank tensors, binary vectors, orthogonal matrices, and matrices formed as the sum of a few permutations. Inspired by the success of the L1-norm and nuclear-norm heuristics, we propose a general convex relaxation framework to recover such simple structured models from partial information. We provide sharp estimates of the number of generic measurements required for exact and robust recovery in a variety of settings. These estimates are based on computing certain Gaussian statistics related to the underlying model geometry. Thus our work extends the catalog of objects and structures (beyond sparse vectors and low-rank matrices) that can be recovered from limited information via tractable convex programming. Joint work with Benjamin Recht, Pablo Parrilo, and Alan Willsky.