Directionlet-based PURE-LET for Poisson Image Denoising

In certain imaging applications, the captured images are corrupted by Poisson noise. For such images, Poisson unbiased risk estimate (PURE) has been proposed as an unbiased estimator of the mean square error between the original and estimated images. By minimizing PURE, noise can be reduced. PURE was originally defined in the Haar wavelet domain. Since the wavelet functions are isotropic in every scale and have limited directional capabilities, t he denoising performance obtained by minimizing PURE is poor around the discontinuities in the images. To overcome these limitations, we extend PURE to the Haar directionlet domain. We show by simulations that minimizing PURE in the directionlet domain results in better denoising performance when compared to minimizing it in the wavelet