The importance of Image quality assessment (IQA) is ever increasing due to the fast paced advances in imaging technology and computer vision. Among the numerous IQA methods, Structural SIMilarity (SSIM) index and its variants are better matched to the perceived quality of the human visual system. However, SSIM methods are insufficiently sensitive, when images contain low information, where the important information only occupies a low proportion of the image while most of the image is noise-like, which is common in scientific data. Therefore, we propose two new IQA methods, InTensity Weighted SSIM index and Low-Information Similarity Index, for such low information images. In addition, auxiliary indexes are proposed to assist with the assessment. The application of these new IQA methods to natural images and field-specific images, such as radio astronomical images, medical images, and remote sensing images, are also demonstrated. The results show that our IQA methods perform better than state-of-the-art SSIM methods for differences in high-intensity parts of the input images and have similar performance to that of the original and gradientbased SSIM for differences in low-intensity parts. Different similarity indexes are suitable for different applications, which we demonstrate in our results.