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HI source finding: 2 novel approaches

ATNF, December 2010


Outline
· Background
· What is source finding? · How do we assess source finders?

· Motivation for developing new HI source finding methods · Novel source finding methods
· · · · General idea Iterative 3-D median smoothing Characterised noise method Wavelet method

· Summary


Background


What is source finding?
· Traditionally, S'Finding has 6 components
· · · · · · Pre-processing Finding source voxels/pixels Recovering extent of each source Merging source components Characterising sources Filtering sources

· Only 1 component is actually source finding!!! · Other components aid/make use of actual source finding


How do we assess source finders?
· Standard criterion
· · · · Reliability = probability of a source being real Completeness = fraction of all sources recovered Source parameters = how accurate are they? This tests end-to-end performance of all 6 components.

· Alternatively
· Only completeness is related to source finder performance · Explicitly use `refined' reliability and completeness · Bias. Are some sources more likely to be detected?


Motivation


Motivation
· ASKAP = high resolution HI data cubes · High resolution means
· Fantastic new science

· Difficulty detecting sources

· Sources are dispersed amongst many voxels
· Voxel S/N is much less than integrated S/N · S/Nvoxel = 2~5 x S/Nsource / # voxels · For instance, 49 < #voxels < 1600 results in 0.05~0.13 < S/N S/Nsource < 0.3~0.7

voxel

/


Motivation
· For bright, compact sources
· Individual voxels have okay/good S/N · Intensity threshold method can (and does!) work

· For extended or faint sources
· Individual voxels have poor S/N · Intensity threshold method unlikely to work · Can be spatially unresolved but extended in frequency

· Intensity thresholding (Duchamp)
· Will be incomplete · Is biassed · Refined reliability suffers trying to improve completeness

· WALLABY needs a source finder that complements Duchamp
· Needs to work on groups of voxels · Should take advantage of high frequency resolution


New source finding methods


Novel source finding: General method
· Treating HI data cube as set of spectra · Pre-process cube with 3-D iterative median smoothing. · For each line of sight
· Combine the neighbouring lines of sight · Use Wavelet analysis and Fourier transform to flatten and remove noise · Identify shapes in processed spectrum using one of:
· · · · Characterised noise method (under investigation) Wavelet analysis (under investigation) Gamma test Intensity threshold

· Merging/Growing · Source characterisation · Source filtering


Iter. 3-D median smoothing: Purpose
· Goal: Reduce noise while preserving shape
· Particularly edges

· Median works because it's non-linear · Consider this,


Iter. 3-D median smoothing: Purpose

· Away from edge
· Median is all signal or all noise

· N e a r a n e d g e
· Contribution of signal and noise is weighted by how many elements lie within filter

· Best to use filter covering odd number of elements · Better to use a filter that's too small than too big


Iter. 3-D median smoothing: Implementation
· Use a 3-D kernel
· Maximises voxels used for median

· 1st pass = immediate neighbours · 2nd pass = sausage in frequency direction
· Highest resolution dimension


Iter. 3-D median smoothing: Results
· Using Duchamp on Paolo Serra's Westerbork test cube
· Find 50% more sources · Less fragmentation of sources · Slightly better/comparable to Duchamp's frequency smoothing/ wavelet analysis

· Confirmed that smoothing scale can't be too large · Combination of smoothing and A'Trous wavelet reconstruction is fantastic!
· Improved reliability, comparable otherwise.


Iter. 3-D median smoothing: Results


Iter. 3-D median smoothing: Results


Characterised noise method
· Datacubes are almost empty
· Robust statistics `almost' solely characterise noise · Robust statistics include the median and the cumulative frequency distribution (c.f.d.)

· For a given line-of-sight
· Noise is described by intensity c.f.d. · A group of pixels will have a statistically significantly different c.f.d. if they contain signal ­ searching for non-noise

· Implementation
· Sliding box-car on different scales · Kuiper or Kolmogorov-Smirnov test

· Advantages
· Ideal for extended sources · Estimates frequency extent

· Limitation
· Correlated noise is selected as a source


Characterised noise method: examples
· 12 lines-of-sight through the WSRT cube, where sources are known to exist
· Good reliability and completeness · Does a good job of recovering frequency extent · Recovers sources amongst noise


Characterised noise method: examples


Characterised noise method: examples
· Blind search for sources in the WSRT cube
· · · · · · · Recovers pretty much all sources Recovers spatial extent No preprocessing applied No line-of-sight stacking used No merging applied No filtering applied Poor implementation


Characterised noise method: examples


Wavelet method
· Compute discrete wavelet transform for multiple basis functions · Select significant wavelet coefficients
· Absolute value cut · Relative cut using standard deviation threshold

· Determine best fitting basis out of significant coefficients · Reconstruct signal using wavelet basis functions and coefficients · Searching for shapes


Wavelet method: wavelet library
· Identified the following wavelets to try
· Removing noise
· Morlet · Meyer

· Finding sources
· · + · · Mexican hat Debauchies mirrored Coiflet Haar

· Debauchies (+ mirrored) should identify double horns robustly


Wavelet method: Examples
· 12 lines-of-sight through the WSRT cube, where sources are known to exist
· · · · · Ability to detect sources is critically dependent upon choice of basis Only detects sources matching basis function Large scales are useless Small scales can be filtered out Blindingly fast!

· Experimenting with best approach for identifying source components · Still working on best way to make use of multiple basis functions


Summary
· 3-D iterative median smoothing works and has benefits for source finding/characterisation · Successful proof-of-concept for
· Characterised noise method · Wavelet method

· Future work
· Improved implementations · Tweaks to both methods · Investigate integration of both methods + intensity thresholding