Fig 2. Same images but with an additive Gaussian noise. The Signal-to-Noise Ration (SNR) is equal to 1.
We have created a set of simulated images by adding a Gaussian white noise with different standard deviations to these two images. The Signal to Noise Ratio (SNR) varies between 0 and 1. For the image with lines, the SNR is defined as the pixel values along the lines divided by the noise standard deviation, and for the image with Gaussians, the SNR is defined as the maximum of the Gaussians divided by the noise standard deviation. 
Fig 3. Kurtosis versus the SNR for the two images using the wavelets (left) and the curvelet (right). Dashed lines represent the images with Gaussians and continuous lines represent the images with lines.
Hence, for each SNR value, we have thirty realizations of the noise, and we have calculated the kurtosis at the different scales of both the curvelet and the wavelet coefficients. These kurtosis values were normalized by the standard deviation of the kurtosis obtained from the wavelet and the curvelet transform of thirty Gaussian white noise realizations. Finally we kept for each SNR the maximum normalized kurtosis along the scales. Fig.3 left (resp. right) shows the normalized kurtosis values using the wavelet transform (resp. the curvelet transform) for the two images (i.e. lines and Gaussians) versus the SNR. Continuous error bars correspond to a one sigma level and dashed error bars correspond to a two sigma level.
We can clearly see that the detection power of the wavevet transform is much larger than the detection power of the curvelet transform for detecting non-Gaussianities due to isotropic features, while curvelets are more powerful than wavelets for detecting anisotropic features.