Improved Denoising of Images Using Modelling of a Redundant Contourlet Transform

In this work we investigate the image denoising problem. One common approach found in the literature involves manipulating the coefficients in the transform domain, e.g. shrinkage, followed by the inverse transform. Several advanced methods that model the inter-coefficient dependencies were developed recently, and were shown to yield significant improvement. However, these methods operate on the transform domain error rather than on the image domain one. These errors are in general entirely different for redundant transforms. In this work we propose a novel denoising method, based on the Basis-Pursuit Denoising (BPDN). Our method combines the image domain error with the transform domain dependency structure, resulting in a general objective function, applicable for any wavelet-like transform. We focus here on the Contourlet Transform (CT) and on a redundant version of it, both relatively new transforms designed to sparsely represent images. The performance of our new method is compared favorably with the state-of-the-art method of Bayesian Least Squares Gaussian Scale Mixture (BLS-GSM), which we adapted to the CT as well, with further improvements still to come.