The AstroStat Slog » compressed sensing

[MADS] compressed sensing

hlee — Fri, 11 Sep 2009 04:20:54 +0000

Soon it’ll not be qualified for [MADS] because I saw some abstracts with the phrase, compressed sensing from arxiv.org. Nonetheless, there’s one publication within refereed articles from ADS, so far.

http://adsabs.harvard.edu/abs/2009MNRAS.395.1733W.
Title:Compressed sensing imaging techniques for radio interferometry
Authors: Wiaux, Y. et al.
Abstract: Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals. We propose new generic imaging techniques based on convex optimization for global minimization problems defined in this context. The versatility of the framework notably allows introduction of specific prior information on the signals, which offers the possibility of significant improvements of reconstruction relative to the standard local matching pursuit algorithm CLEAN used in radio astronomy. We illustrate the potential of the approach by studying reconstruction performances on simulations of two different kinds of signals observed with very generic interferometric configurations. The first kind is an intensity field of compact astrophysical objects. The second kind is the imprint of cosmic strings in the temperature field of the cosmic microwave background radiation, of particular interest for cosmology.

As discussed, reconstructing images from noisy observations is typically considered as an ill-posed problem or an inverse problem. Owing to the personal lack of comprehension in image reconstruction of radio interferometry observation based on sample from Fourier space via inverse Fourier transform, I cannot judge how good this new adaption of compressed sensing for radio astronomical imagery is. I think, however, compressed sensing will take over many of traditional image reconstruction tools due to their shortage in forgiving sparsely represented large data/images .

Please, check my old post on compressed sensing for more references to the subject like the Rice university repository in addition to references from Wiaux et al. It’s a new exciting field with countless applications, already enjoying wide popularity from many scientific and engineering fields. My thought is that well developed compressed sensing algorithms might resolve bandwidth issues in satellite observations/communication by transmiting more images within fractional temporal intervals for improved image reconstruction.

[ArXiv] Sparse Poisson Intensity Reconstruction Algorithms

hlee — Thu, 07 May 2009 16:14:39 +0000

One of [ArXiv] papers from yesterday whose title might drag lots of attentions from astronomers. Furthermore, it’s a short paper.
[arxiv:math.CO:0905.0483] by Harmany, Marcia, and Willet.

Estimating f under “Sparse Poisson Intensity” condition is an frequently appearing topic in high energy astrophysics data analysis. Some might like to check references in the paper, which offer solutions to compressed sensing problems with different kinds of sparsity, minimization approaches, and constraints on f.

Apart from the technical details, the first two sentences from the conclusion,

We have developed computational approaches for signal reconstruction from photon-limited measurements – a situation prevalent in many practical settings. Our method optimizes a regularized Poisson likelihood under nonnegativity constraints

tempt me to study and try their algorithm.

[ArXiv] 1st week, Feb. 2008

hlee — Sun, 10 Feb 2008 16:56:12 +0000

Review papers on Bayesian hierarchical modeling and LAR (least angle regression) appeared in this week’s stat arXiv and in addition to interesting astro-ph papers.

A review paper on LASSO and LAR: [stat.ME:0801.0964] T. Hesterberg et.al.
Least Angle and L₁ Regression: A Review
Model checking for Bayesian hierarchical modeling: [stat.ME:0802.0743] M. J. Bayarri, M. E. Castellanos
Bayesian Checking of the Second Levels of Hierarchical Models

[astro-ph:0802.0042] Y. Kubo
Statistical Models for Solar Flare Interval Distribution in Individual Active Regions (it discusses AIC)
[astro-ph:0802.0131] J.Bobin, J-L Starck and R. Ottensamer
Compressed Sensing in Astronomy
[astro-ph:0802.0387] J. Gaite
Geometry and scaling of cosmic voids
[astro-ph:0802.0400] R. Vio & P. Andreani
A Modified ICA Approach for Signal Separation in CMB Maps
[astro-ph:0802.0498] V. Balasubramanian, K. Larjo and R. Sheth
Experimental design and model selection: The example of exoplanet detection
[astro-ph:0802.0537] G. Dan, Z. Yanxia, & Z. Yongheng
Support Vector Machines and Kd-tree for Separating Quasars from Large Survey Databases

compressed sensing and a blog

hlee — Thu, 25 Oct 2007 01:15:52 +0000

My friend’s blog led me to Terrence Tao’s blog. A mathematician writes topics of applied mathematics and others. A glance tells me that all postings are well written. Especially, compressed sensing and single pixel cameras drags my attention more because the topic stimulates thoughts of astronomers in virtual observatory^[1] and image processing^[2] (it is not an exaggeration that observational astronomy starts with taking pictures in a broad sense) and statisticians in multidimensional applications, not to mention engineers in signal and image processing.

A particular interest of mine from his post is that compressed sensing could resolves bandwidth problems in astronomy and consequential sequential analysis on astronomical data (streaming data analysis). Overall, his list of applications at the end may enlighten scientists probing the sky with different waveband telescopes.

see the slog posting “Virtual Observatory”
see the slog posting “The power of wavedetect”