The need of source separation methods in astronomy has led various adaptations of decomposition methods available. It is not difficult to locate those applications from journals of various fields including astronomical journals. However, they are most likely soliciting one dimension reduction method of their choice over others to emphasize that their strategy works better. I rarely come up with a paper which gathered and summarized component separation methods applicable to astronomical data. In that regards, the following paper seems useful to overview methods of reducing dimensionality for astronomers.

[arxiv:0805.0269]
Component separation methods for the Planck mission
S.M.Leach et al.
Check its appendix for method description.

Various library/modules are available through software/data analysis system so that one can try various dimension reduction methods conveniently. The only concern I have is the challenge of interpretation after these computational/mathematical/statistical analysis, how to assign physics interpretation to images/spectra produced by decomposition. I think this is a big open question.

[arxiv:0906.3662] The Statistical Analysis of fMRI Data by Martin A. Lindquist
Statistical Science, Vol. 23(4), pp. 439-464

This review paper offers some information and guidance of statistical image analysis for fMRI data that can be expanded to astronomical image data. I think that fMRI data contain similar challenges of astronomical images. As Lindquist said, collaboration helps to find shortcuts. I hope that introducing this paper helps further networking and collaboration between statisticians and astronomers.

List of similarities

• data acquisition: data read in frequency domain and image reconstruction via inverse Fourier transform. (To my naive eyes, It looks similar to Power Spectrum Analysis for cosmic microwave background (CMB) data).
• amplitudes or coefficients are cared and analyzed, not phase nor wavelets.
• understanding data:brain physiology or physics like cosmological models that describe data generating mechanism.
• limits in/trade-off between spatial and temporal resolution.
• understanding/modeling noise and signal.

These similarities seem common for statistically analyzing images from fMRI or telescopes. Notwithstanding, no astronomers can (or want) to carry out experimental design. This can be a huge difference between medical and astronomical image analysis. My emphasis is that because of these commonalities, strategies in preprocessing and data analysis for fMRI data can be shared for astronomical observations and vise versa. Some sloggers would like to check Section 6 that covers various statistical models and methods for spatial and temporal data.

I’d rather simply end this posting with the following quotes, saying that statisticians play a critical role in scientific image analysis.

There are several common objectives in the analysis of fMRI data. These include localizing regions of the brain activated by a task, determining distributed networks that correspond to brain function and making predictions about psychological or disease states. Each of these objectives can be approached through the application of suitable statistical methods, and statisticians play an important role in the interdisciplinary teams that have been assembled to tackle these problems. This role can range from determining the appropriate statistical method to apply to a data set, to the development of unique statistical methods geared specifically toward the analysis of fMRI data. With the advent of more sophisticated experimental designs and imaging techniques, the role of statisticians promises to only increase in the future.

A full spatiotemporal model of the data is generally not considered feasible and a number of short cuts are taken throughout the course of the analysis. Statisticians play an important role in determining which short cuts are appropriate in the various stages of the analysis, and determining their effects on the validity and power of the statistical analysis.

• [astro-ph:0806.0650] Kimball and Ivezi\’c
  A Unified Catalog of Radio Objects Detected by NVSS, FIRST, WENSS, GB6, and SDSS (The catalog is available HERE. I’m always fascinated with the possibilities in catalog data sets which machine learning and statistics can explore. And I do hope that the measurement error columns get recognition from non astronomers.)

• [astro-ph:0806.0820] Landau and Simeone
  A statistical analysis of the data of Delta \alpha/ alpha from quasar absorption systems (It discusses Student t-tests from which confidence intervals for unknown variances and sample size based on Type I and II errors are obtained.)

• [stat.ML:0806.0729] R. Girard
  High dimensional gaussian classification (Model based – gaussian mixture approach – classification, although it is often mentioned as clustering in astronomy, on multi- dimensional data is very popular in astronomy)

• [astro-ph:0806.0520] Vio and Andreani
  A Statistical Analysis of the “Internal Linear Combination” Method in Problems of Signal Separation as in CMB Observations (Independent component analysis, ICA is discussed)

• [astro-ph:0806.0560] Nobel and Nowak
  Beyond XSPEC: Towards Highly Configurable Analysis (The flow of spectral analysis with XSPEC and Sherpa has not been accepted smoothly; instead, it has been a personal struggle. It seems the paper considers XSPEC as a black box, which I completely agree with. The main objective of the paper is comparing XSPEC and ISIS)

• [astro-ph:0806.0113] Casandjian and Grenier
  A revised catalogue of EGRET gamma-ray sources (The maximum likelihood detection method, which I never heard from statistical literature, is utilized)

• [astro-ph:0803.3154]B. G. Elmegreen
  The Stellar Initial Mass Function in 2007: A Year for Discovering Variations

• [astro-ph:0803.3260]J.K. Lawrence, A.C. Cadavid & A. Ruzmaikin
  Rotational quasi periodicities and the Sun – heliosphere connection (I wish arxiv provides keywords. My keywords to this preprint are solar cycle, Lomb-Scargle periodogram, PCA, ICA, all interesting to CHASC folks. Particularly, I felt some similarity to one of stat310 talks about Gravity Probe B)

• [astro-ph:0803.3775] L. Samushia, & B. Ratra
  Constraints on Dark Energy from Galaxy Cluster Gas Mass Fraction versus Redshift data (another example of Monte Carlo Markov Chain, not Markov chain Monte Carlo in the abstract but MCMC is not their research focus)

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