#### [MADS] multiscale modeling

A few scientists in our group work on estimating the intensities of gamma ray observations from sky surveys. This work distinguishes from typical image processing which mostly concerns the point estimation of intensity at each pixel location and the size of overall white noise type error. Often times you will notice from image processing that the orthogonality between errors and sources, and the white noise assumptions. These assumptions are typical features in image processing utilities and modules. On the other hand, CHASC scientists relate more general and broad statistical inference problems in estimating the intensity map, like intensity uncertainties at each point and the scientifically informative display of the intensity map with uncertainty according to the Poisson count model and constraints from physics and the instrument, where the field, **multiscale modeling** is associated.

As the post title [MADS] indicates, no abstract has keywords **multiscale modeling.** It seems like that just the jargon is not listed in ADS since “multiscale modeling” is practiced in astronomy. One of examples is our group’s work. Those CHASC scientists take Bayesian modeling approaches, which makes them unique to my knowledge in the astronomical society. However, I expected constructing an intensity map through statistical inference (estimation) or “multiscale modeling” to be popular among astronomers in recent years. Well, none came along from my abstract keyword search.

Wikipedia also shows a very brief description of **multiscale modeling** and emphasized that it is a fairly new interdisciplinary topic. wiki:multiscale_modeling. TomLoredo kindly informed me some relevant references from ADS after my post [MADS] HMM. He mentioned his search words were **Markov Random Fields** which can be found from __ stochastic geometry__ and

__in addition to many applications in computer science. Not only these publications but he gave me a nice comment on analyzing astronomical data, which I’d rather postpone for another discussion.__

*spatial statistics*- Quantifying Doubt and Confidence in Image “Deconvolution” by Connors, Alanna; van Dyk, D.; Chiang, J.; CHASC
- Blind Bayesian restoration of adaptive optics telescope images using generalized Gaussian Markov random field models by Jeffs, Brian D.; Christou, Julian C.
- Segmenting Chromospheric Images with Markov Random Fields (paper in SCMA II) Turmon, Michael J.; Pap, Judit M.
- Bayesian deconvolution methods in astronomy by Molina, R.; Katsaggelos, A. K.; Mateos, J
- Compound Gauss-Markov random fields for astronomical image restoration by Molina, R.; Katsaggelos, A. K.; Mateos, J.; Abad, J
- Markov random field applications in image analysis by Jain, A. K.; Nadabar, S. G (I bet “Jain” is the author of many celebrated papers in image processing and machine learning. I often find that well known computer scientists involve in astronomical researches ).

The reason I was not able to find these papers was that they are not published in the 4 major astronomical publications + Solar Physics. The reason for this limited search is that I was overwhelmed by the amount of unlimited search results including arxiv. (I wonder if there is a way to do exclusive searches in ADS by excluding arxiv:comp, arxiv:phys, arxiv:math, etc). Thank you, Tom, for providing me these references.

Please, check out CHASC website for more study results related to “multiscale modeling” from our group.

**[Added]** Nice tutorials related to Markov Random Fields (MRF) recommended by an expert in the field and a friend (all are pdfs).

## vlk:

12-17-2008, 4:21 pmMultiscale modelingis not an oft-used term in astro literature, but people have been applying multiscale analysis for decades. Wavelets have been quite popular, for instance. See, e.g., cite list for the Wavdetect paper. Alex Young has also been pioneering the use of Curvelets in solar image analysis. Strictly speaking, it is notmodelingas understood by Bayesians, but nevertheless it shows that astronomers are aware of the concepts.