Figure 1

The left column shows the PDFs of one convergence map we constructed with two levels of noise added. The right column shows the PDFs of the convergence map with noise reduction by the Wiener filter. The PDFs of the field after the Gaussianization are also plotted (dotted line), which is just the standard Gaussian distribution by definition. From the PDFs we can see that the Gaussian noises of both levels dominate the distribution. After the Wiener filter is applied, the non-Gaussianity is recovered to some extent.Reuse & Permissions

Figure 2

The left panel shows the Gaussian transformations from the noisy $\kappa$ to Gaussian $y$ field, for 20 realizations. The right panel shows the result after the noise is reduced by the Wiener filter. The heavy noise makes the Gaussian transformations of trivial-mapping ($y=\kappa$). Only a few pixels survive in case A. For the noise-reduced case, we can see the effect of the Wiener filter from the shape of the Gaussian transformation. The 20 Gaussian transformations converge with each other for noisy maps, and are in reasonable agreement with each other for the noise-reduced case. The small divergence in the latter case arises from the different normalization factors determined at the zero point. Nevertheless, the normalization factor will not influence the non-Gaussianity measures.Reuse & Permissions

Figure 3

The ensemble averaged skewness (top) and kurtosis (bottom) of the smoothed noisy (left) and the Wiener filtered (right) convergence maps are plotted in a solid line as a function of smoothing scale for case A. The results of the Gaussianized fields are plotted in a dotted line with a little horizontal shift for clarity. The error bars are the rms dispersions among 20 realizations. The Gaussianization cannot reduce the skewness and kurtosis of these noisy maps to an acceptable level. However, we find that the Wiener filter is efficient in reducing the shape measurement noise. For the Wiener filtered maps, the Gaussianization can suppress the skewness and kurtosis towards zero for all the smoothing scales we considered. The statistical errors are quite correlated, since $K_n$ at different smoothing scales share much of the same cosmic volume, and hence much the same cosmic variance and measurement noise.Reuse & Permissions

Figure 4

The ensemble averaged 5th- (top) and 6th-order (bottom) cumulants of the smoothed noisy (left) and noise-reduced (right) convergence maps are plotted in a solid line as a function of smoothing scale for case A. The results of the Gaussianized fields are plotted in a dotted line with a little horizontal shift for clarity. The correlated error bars are the rms dispersions among the 20 realizations. The Gaussianization cannot reduce the 5th- and 6th-order cumulants of these noisy maps to an acceptable level. When the noise is reduced by the Wiener filter, the Gaussianization can suppress the 5th- and 6th-order cumulants to zero for all the smoothing scales we considered.Reuse & Permissions

Figure 5

The ensemble averaged skewness (top) and kurtosis (bottom) of the smoothed noisy (left) and noise-reduced (right) convergence maps are plotted in a solid line as a function of smoothing scale for case B. The results of the Gaussianized fields are plotted in a dotted line. The correlated error bars are the rms dispersions among the 20 realizations. The Gaussianization cannot reduce the skewness and kurtosis of these noisy maps to an acceptable level. When the noise is reduced by the Wiener filter, the Gaussianization can suppress the kurtosis towards zero for all the smoothing scales we considered. But for the skewness, we still see residual non-Gaussianity. The results for an inaccurate noise spectrum estimation used in the Wiener filtering are presented as dashed and dot-dashed lines. A factor of 2 overestimation or underestimation does not change the Gaussianization performance much.Reuse & Permissions

Figure 6

The ensemble averaged 5th- (top) and 6th-order (bottom) cumulants of the smoothed noisy (left) and noise-reduced (right) convergence maps are plotted in a solid line, as a function of smoothing scale for case B. The results of the Gaussianized fields are plotted in a dotted line. The correlated error bars are the rms dispersions among the 20 realizations. The Gaussianization cannot reduce the 5th- and 6th-order cumulants of these noisy maps to an acceptable level. When the noise is reduced by the Wiener filter, the Gaussianization can suppress the 5th- and 6th-order cumulants to zero for all the smoothing scales we considered. The results for an inaccurate noise spectrum estimation used in the Wiener filtering are presented as dashed and dot-dashed lines. A factor of 2 overestimation or underestimation does not change the Gaussianization performance much.Reuse & Permissions

Figure 7

The ratios of the $n$-th-order cumulants of the smoothed noisy (left) and noise-reduced (right) convergence maps from prior to the Gaussianization to afterwards, as functions of smoothing scale for case A (top) and B (bottom). The Gaussianization can only suppress by a factor of 2 for the skewness of a noisy map, and a little more or less for higher-order cumulants. When the noise is reduced by the Wiener filter, the Gaussianization can suppress by a factor of 5 for the skewness of a noisy map, and more than 10 for higher-order cumulants.Reuse & Permissions

Figure 8

The ensemble averaged reduced bispectrum $q(\ell ,u,\alpha )$ of the noisy convergence maps for case B on the same 9 configurations as the previous work. The $q$’s prior to the Gaussianization are presented in a solid line, while the afterwards is in a dotted line with a horizontal shift for clarity. The error bars are the rms dispersions over 20 respective maps. The Gaussianization can only suppress the bispectrum by a small factor, and a large amount of non-Gaussianity still remains in bispectrum of the new field.Reuse & Permissions

Figure 9

The ensemble averaged reduced bispectrum $q(\ell ,u,\alpha )$ of the noise-reduced convergence maps for case B, on the same 9 configurations. The $q$’s prior to the Gaussianization are presented in a solid line and those afterwards in a dotted line with a horizontal shift for clarity. The error bars are the rms dispersions over 20 respective maps. The recovery effect of the Wiener filter results in a larger value in the bispectrum. The Gaussianization after noise reduction can suppress the bispectrum more, and on many configurations the bispectrum afterwards is close to zero within error bars; however, there still exists some amount of non-Gaussianity on small scale configurations. The results for an inaccurate noise power spectrum estimation used in the Wiener filtering are presented in dashed and dot-dashed lines, for cases of a factor of 2 overestimation or underestimation in the noise power spectrum. The results show that, even for these extreme cases, the Gaussianization performance remains impressive.Reuse & Permissions