Translation invariant combined denoising algorithm

The paper develops a method for denoising images corrupted with additive white Gaussian noise (AWGN). The noise degrades the image quality and makes the interpretation, analysis and segmentation of images harder. The discrete curvelet transform is a new image representation approach that codes image edges more efficiently than the wavelet transform. On the other hand, the wavelet transform codes homogeneous areas better than the curvelet transform. A translation invariant combined denoising algorithm (TICDA) is proposed. The algorithm is implemented by combining the undecimated discrete wavelet transform (UDWT) and the translation invariant discrete curvelet transform (TIDCT). The AWGN image is then denoised by letting the TICDA solve an l₁ optimization problem.