Imaging and Computing Seminar — Fall 2011
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Th 09/29, at 4:30pm, in room 2-142
Shravan Hanasoge, Geosciences, Princeton.
Noise Tomography of the 3-D interior of the Sun and Earth
Abstract: Solar Oscillations, similar to Earth noise, are excited stochastically. Statistical averages of cross correlations of the surface velocity field of the Sun, observed at nearly 16 million points, show the presence of seismic signals, allowing us to measure wave travel times and amplitudes. I will describe techniques of PDE-constrained optimization that are applied to retrieve the gradient of the measurement misfit and show examples of sensitivity kernels. These developments render possible the accurate imaging of sub-surface magnetic fields and convection in the Sun and I will present recent work along these lines. Time permitting, I shall also show preliminary results pertaining to the localization of Earth-noise sources.
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Th 10/13, at 4:30pm, in room 2-142
Sebastien Leprince, Geological and Planetary Sciences, Caltech.
Environmental Monitoring from Space using Optical Imagery: The Versatility of Sub-Pixel Image Matching
Group website, Imagin'Labs website.
Abstract: COSI-Corr is a suite of algorithms for precise “Co-registration of Optically Sensed Images and Correlation,” which was developed within the Division of Geological and Planetary Sciences at Caltech and was first released to the academic community in 2007. Its capability to accurately monitor the Earth's surface deformation using satellite or aerial imagery has since proved useful for a wide variety of applications. I will present the fundamental principles of COSI-Corr, which are the key ingredients to achieve sub-pixel registration and sub-pixel measurement accuracy between multi-temporal images. In particular, I will show how these principles can be applied to various types of images to extract 2D, 3D, or even 4D deformation fields of a given surface. Examples are drawn from recent collaborative studies and include: (1) The study of the Icelandic Krafla rifting crisis that occurred from 1975 to 1984 where we used a combination of archived airborne photographs, declassified spy satellite imagery, and modern satellite acquisitions to propose a detailed 2D displacement field of the ground; (2) The estimation of glacial velocities; (3) The derivation of sand ripples migration rates on Mars using HiRISE imagery; (4) The estimation of ocean swell; (5) The derivation of the 3D ground displacement field induced by the 2010 Mw 7.2 El Mayor- Cucapah Earthquake, as recorded from pre- and post-event LiDAR acquisitions; (6) And, a new space mission concept, in partnership with the NASA Jet Propulsion Laboratory, where sub-pixel image matching could be used to image the propagation of seismic waves at the surface of the Earth. Finally, I will highlight the potential for applying these techniques on a large scale to provide global monitoring of our environment.
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Th 10/27, no seminar
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Th 11/03, at 4:30pm, in room 2-142
Jianfeng Lu, CIMS, NYU
Efficient basis set for Kohn-Sham density functional theory
Abstract: Kohn-Sham density functional theory (DFT) is one of the most widely used models for electronic structure calculations. The conventional algorithms for Kohn-Sham DFT are however quite expensive which limit the applicability. We aim at development of efficient algorithms to extend ab initio calculation based on Kohn-Sham DFT to larger systems. In this talk, we will discuss recent progress in designing efficient basis set for Kohn-Sham DFT. The proposed method captures the oscillatory behavior of the solution by numerical obtained basis set from solution to local auxiliary problem. The strategy can be also applied to other problems in scientific computing involving local rough coefficients. (Joint work with Weinan E, Lin Lin, and Lexing Ying)
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Th 11/10, at 3:15pm, in room 2-136
Marco Duarte, Electrical and computer engineering, UMass Amherst.
Recovery of Frequency-Sparse Signals from Compressive Measurements
Abstract: Compressive sensing (CS) is a new approach to simultaneous sensing and compression of sparse and compressible signals based on randomized dimensionality reduction. To recover a signal from its compressive measurements, standard CS algorithms seek the sparsest signal in some discrete basis or frame that agrees with the measurements. A great many applications feature smooth or modulated signals that are frequency sparse and can be modeled as a superposition of a small number of sinusoids. Unfortunately, such signals are only sparse in the discrete Fourier transform (DFT) domain when the sinusoid frequencies live precisely at the center of the DFT bins; when this is not the case, CS recovery performance degrades significantly.
This talk will introduce a spectral compressive sensing (SCS) recovery framework for arbitrary frequency sparse signals. The key ingredients are an over-sampled DFT frame, a signal model that inhibits closely spaced sinusoids, and classical sinusoid parameter estimation algorithms from the field of spectral estimation. Using periodogram and line spectral estimation methods, we demonstrate that SCS significantly outperforms current state-of-the-art CS algorithms based on the DFT while providing provable bounds on the number of measurements required for stable recovery.
This is joint work with Richard G. Baraniuk.
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Mo 11/21, at 4:30pm, in room 2-142
Pierre Garapon, Mathematics, Stanford.
Mathematical resolution in imaging sources and small objects
Abstract: In this presentation I will start by making a few remarks on source localization, when measuring the field on a sphere. We will see that accuracy of the localization in mainly given by the wave number, but also that the situation is very different when measuring data in the volume of the domain. We will try to generalize this example by considering the scattering by a small object, and we will study numerical illustration in the case of elasticity imaging.
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Th 12/01, at 4:30pm, in room 2-142
Vivek Goyal, EECS, MIT.
Compressive Depth Acquisition Cameras: Principles and Demonstrations
Abstract: Measuring time elapsed from transmitting a pulse to receiving a reflected response is a standard method for distance estimation. Light detection and ranging (LIDAR) systems and time-of-flight (TOF) cameras use this principle along with scanning by the illumination source or 2D sensor arrays to acquire depth maps. This talk introduces depth map acquisition with high spatial and range resolution using a single, omnidirectional, time-resolved photodetector and no scanning components. In contrast to compressive photography, the information of interest -- scene depths -- is nonlinearly mixed in the measured data. The reconstruction uses parametric signal modeling to recover a set of depths present in the scene. Then, a convex optimization formulation that exploits sparsity of the Laplacian of the depth map of a typical scene is used to determine correspondences between spatial positions and depths.
We have demonstrated depth map reconstruction for both near and medium-range scenes even in low light conditions. An initial prototype uses patterned illumination created by a 64-by-64-pixel spatial light modulator. With this prototype, we constructed depth maps of scenes comprising two to four planar shapes using only 205 spatially-patterned, pulsed illuminations of the scene. A second apparatus achieves spatially-patterned reception with a digital micromirror device and a single photon-counting detector. With the same mathematical framework, we constructed depth maps with and without the presence of a partially-transmissive occluder.
Joint work with Ahmed Kirmani, Andrea Colaco, Greg Howland, John Howell, and Franco Wong.