General CMB bispectrum analysis using wavelets and separable modes

In this paper we combine partial-wave (modal'') methods with a wavelet analysis of the cosmic microwave background bispectrum. While utilizing a wavelet-based estimator, we demonstrate that it is possible-via a change of basis matrix-to express the estimator in terms of partial waves. Our implementation allows one to exploit the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain the amplitude of arbitrary primordial bispectra. In particular the methodology introduced here allows for a change of basis from the space of cubic wavelet statistics to partial waves, which have proven particularly useful for investigating the underlying shape governing the non-Gaussian signal. This will be particularly important for upcoming surveys such as Planck. A key advantage is the computational efficiency of calculating the inverse covariance matrix in wavelet space, producing an error bar which is close to optimal. We verify the efficacy and robustness of the method by applying it to WMAP7 data, finding f(NL)(loc) 35.3 +/- 23.6 and f(NL)(eq) = -160.6 +/- 123.6, after correcting for unresolved point sources.