Image Processing - Does PSNR and SSIM metrics show smoothing (noise reduction) quality?

For my Image Processing class project, I am filtering an image with various filter algorithms (bilateral filter, NL-Means etc..) and trying to compare results with changing parameters. I came across PSNR and SSIM metrics to measure filter quality but could not fully understand what the values mean. Can anybody help me about:

Does a higher PSNR value means higher quality smoothing (getting rid of noise)?
Should SSIM value be close to 1 in order to have high quality smoothing?
Are there any other metrics or methods to measure smoothing quality?

I am really confused. Any help will be highly appreciated. Thank you.

Solution

With respect to an ideal result image, the PSNR computes the mean squared reconstruction error after denoising. Higher PSNR means more noise removed. However, as a least squares result, it is slightly biased towards over smoothed (= blurry) results, i.e. an algorithm that removes not only the noise but also a part of the textures will have a good score.

SSIm has been developed to have a quality reconstruction metric that also takes into account the similarity of the edges (high frequency content) between the denoised image and the ideal one. To have a good SSIM measure, an algorithm needs to remove the noise while also preserving the edges of the objects.

Hence, SSIM looks like a "better quality measure", but it is more complicated to compute (and the exact formula involves one number per pixel, while PSNR gives you an average value for the whole image).