The traditional correlation measures are not suitable for noisy or those with outliers. Non-parametric methods like Kendall and Spearman can do slightly better job than Pearson but not enough.
The R package robust provides nice robust correlation methods, covRob:
R LINK
Other robust methods can be found here:
Robust Task View
For outlier removal, you may refer to outliers package. Honestly, it's not doing a good job at all.
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