General information
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Code name:
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CVN Fourier
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Code author:
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Reshad Hosseini and Matthias Bethge
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| Code url: |
http://great08challenge.pbworks.com/f/Great-Challenge.zip |
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Method summary:
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A new shear estimation method using the power spectrum as an unbiased statistic of individual galaxy images |
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More information:
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In this work, we present a new method for the estimation of shear of a set of galaxies with unkown shapes. Common procedures first compute an estimate of some characteristic features for each individual galaxy and then average over these. As the average becomes independent of the individual galaxy shapes with increasing number of galaxies, it can be used as an estimator of the shear. To the best of our knowledge, however, the feature estimates used by all existing methods are biased. Even in a stacking procedure where the characteristic feature is a galaxy image that has been shifted such that the galaxy centers are at the same location in all images, the resulting estimate still depends on the shape of the galaxy, because the shape influences the estimate of the mean.
Here we introduce the magnitude of the Fourier transform of the galaxy raised to an abitrary power as a characteristic feature of the individual galaxies. This feature is completely independent of the location where the galaxy centers are located in the individual images provided the smoothed galaxy intensities decay sufficiently fast. No other assumptions are necessary. If the galaxy images are contaminated by Poisson noise, an unbiased estimator of the power spectrum is given by the power spectrum of the noisy image minus a constant. The resulting image obtained by averaging over the unbiased estimators of the individual galaxy power spectra is an elliptically contoured function multiplied by the power spectrum of the convolution kernel plus Gaussian noise. After suitable normalization, the square root of the covariance matrix of the elliptically contoured function is equal to the shear coordinate transformation matrix. For parameter fitting, we used a weighted non-linear least square method for which the weights are equal to the inverse of the standard deviation of the noise. |
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Programming language:
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MATLAB
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Required libraries:
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Optimization Toolbox
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| Relation to GREAT08: |
No relation to the GREAT08 Team. Winner of the prize for highest Q value. |
Information specific to latest implementation for GREAT08 Challenge LowNoise_Blind
N/A
Information specific to latest implementation for GREAT08 Challenge RealNoise_Blind
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url for specific code:
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Great-Challenge.zip |
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Runtime per galaxy:
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1 sec for each galaxy |
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Q from leaderboard:
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210.9
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Date of leaderboard submission:
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Tue 28 Apr 2009
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Information specific to earlier implementations for GREAT08 Challenge:
N/A
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