In this work it is demonstrated that computationally efficient deniosing can be done using thresholding of wavelet coefficients without sacrificing image quality relative to state-of-the-art patch-based methods. This is achieved by combining use of a redundant, directional tight wavelet frame with the Karhunen-Loeve transform along the "directions" dimension. An efficient GPU implementation of the algorithm required less than 30 seconds to process even relatively large DTI datasets (e.g. 96x96x60x203). The proposed approach should find use in SNR-challenged acquisitions such high resolution DTI, DKI and DSI.