Image Denoising with the Contourlet Transform

In this work the image denoising problem is examined. A common approach involves transform-domain coefficients manipulation, followed by the inverse transform. This approach is highlighted by recently-developed methods that model the inter-coefficient dependencies. However, these methods operate on the transform domain error rather than on the more relevant image domain one. In this work we propose a novel denoising method, based on the BasisPursuit Denoising (BPDN) method. Our method combines the image domain error with the transform domain dependency structure, resulting in a general objective function, applicable for any waveletlike transform. We focus here on the Contourlet Transform (CT), a relatively new transform designed to sparsely represent images. The superiority of our method over BPDN is demonstrated, thus providing a more advanced tool for image restoration.