One of them is curvelets, a strange version of "sharp-looking, angular" wavelets. Here is an example of a curvelet at the research page of Harry Hess.
A poster on Thursday, "R.Sivakumar, T. Aparna, Aruna Swaminathan, and V. Divya (Sri Krishna College of Engineering and Technology). Medical image denoising using curvelet transform". They used "WRAPPING" version of the CurveLab software (there is also "USFFT" version), available at
They reported better image compression and better quality of the restored pictures, and also better removal of random and Gaussian noise, than with more traditional wavelets. There was no difference for "salt-and-pepper" noise, and traditional wavelets were better with "speckled" noise.