Wednesday, June 16, 2010

CS: CS SPDE, Cramér-Rao Bound In Noisy CS, Compressive Fourier Transform Spectroscopy, compressive terahertz imaging and a job at Exxon

Here are four papers that showed up on my radar screen and finally a job from ExxonMobil:

A non-adapted sparse approximation of PDEs with stochastic inputs by Alireza Doostan, Houman Owhadi. The abstract reads:
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems (with slow decay in the spectrum).

Recently, it has been proved in [Babadi et. al., 2009] that in noisy compressed sensing, a joint typical estimator can asymptotically achieve the Cram\'er-Rao lower bound of the problem. To prove this result, [Babadi et. al., 2009] used a lemma, which is provided in [Akackaya et. al., 2008], that comprises the main building block of the proof. This lemma contains a mathematical mistake in its statement and proof which should be corrected. One wonders then whether or not the main results of [Babadi et. al., 2009] are correct. In this correspondence, we will first explain the mistake in the mentioned lemma in [Akackaya et. al., 2008] and will then state a new correct form of it. Then we re-study the main results of [1], and we will show that fortunately they remain valid, that is, the Cram\'er-Rao bound in noisy compressed sensing is achievable and a joint typical estimator can achieve it.

Compressive Fourier Transform Spectroscopy by Ori Katz, Jonathan M. Levitt, Yaron Silberberg. The abstract reads:
We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N time-domain measurements using a compressive-sensing reconstruction algorithm. We demonstrate the technique by resolving sparse vibrational spectra using less than 25% of the Nyquist rate samples in single-pulse CARS experiments. The method requires no modifications to the experimental setup and can be directly applied to any Fourier-transform spectroscopy measurement, in particular multidimensional spectroscopy.

And behind a paywall: Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging by Zhimin Xu and Edmund Y. Lam. The abstract reads:
Terahertz (THz) time-domain imaging is an emerging modality and has attracted a lot of interest. However, existing THz imaging systems often require a long scan time and sophisticated system design. Recently, a new design incorporating compressed sensing (CS) leads to a lower detector cost and shorter scan time, in exchange for computation in an image reconstruction step. In this paper, we develop two reconstruction algorithms that can estimate the underlying scene as accurately as possible. First is a single-band CS reconstruction method, where we show that by making use of prior information about the phase and the correlation between the spatial distributions of the amplitude and phase, the reconstruction quality can be significantly improved over previously published methods. Second, we develop a method that uses the multi-frequency nature of the THz pulse. Through effective use of the spatial sparsity, spectroscopic phase information, and correlations across the hyperspectral bands, our method can further enhance the recovered image quality. This is demonstrated by computation on a set of experimental THz data captured in a single-pixel THz system.

A job at Exxon:

AutoReqId 9655BR
Job or Campus Folder Research Scientist-Inversion Methods
Job Description ExxonMobil’s Corporate Strategic Research laboratory is seeking applications from talented individuals in physics, applied mathematics, or engineering with a strong record of achievements in fields related to non-linear inversion, compressive sensing, and their associated mathematical and numerical methods. Specific position is in the following areas of interest:

Research Scientist – Inversion methods and compressive sensing. Position involves developing algorithms involved in large-scale non-linear inversion. Candidates with experience with the mathematics of compressive sensing, signal/image processing, denoising, sub-Nyquist signal reconstruction, and sparse representation of data desired.

Job Requirements:

Applicants should have a Ph.D. in applied mathematics, physics, engineering, geophysics, or a related field, with a strong ability in their field of expertise. Proficiency with scientific programming languages and experience with large-scale, parallel, numerical simulations are definite advantages. The ability to communicate and interact with internal and external groups will be an important selection criterion. Candidates should have a strong publication record, excellent oral presentation and writing skills, and show a desire and ability to grow into new science areas.

The successful candidate will join a dynamic, multi-disciplinary group of world-class scientists who focus on performing breakthrough research and creating new approaches to solve our most challenging problems. Technical staff members in this position implement and report on independent research, participate in program development, as well as collaborate internationally with leading engineers and scientists from industry, universities, and other technical institutions.

ExxonMobil’s Corporate Strategic Research (CSR) laboratory is a powerhouse in energy research focusing on fundamental science that can lead to technologies having a direct impact on solving our biggest energy challenges. Our facilities are centrally located in scenic Annandale, New Jersey, approximately one hour from both New York City and Philadelphia.

ExxonMobil offers an excellent working environment and a competitive compensation and benefits package.

ExxonMobil is an Equal Opportunity Employer
Job Location Clinton, NJ

1 comment:

Mehmet said...

Dear Igor,

While reading your blog, I came across the paper "On the Achievability of Cramér-Rao Bound In Noisy Compressed Sensing," which claimed there was a mistake in one of our earlier works. I have contacted the authors of the work and clarified their source of confusion.

Our proof IS correct as it was published. Just wanted to let the community know :)

Thanks for running this blog, so that we become aware of such misunderstandings early on.

Thanks
Mehmet