Perceptual soft thresholding using the structural similarity index

In this paper, we present a novel algorithm for wavelet domain image denoising using the soft thresholding function. The thresholds are designed to be locally optimal with respect to the structural similarity (SSIM) index. The SSIM Index is first expressed in terms of wavelet transform coefficients of orthogonal wavelet transforms. The wavelet domain representation of the SSIM Index, along with the assumption of a Gaussian prior for the wavelet coefficients is used to formulate the soft thresholding optimization problem. A locally optimal solution is found using a quasi-Newton approach. This solution is applied to denoise images in the wavelet domain. The visual quality of the images denoised using the proposed algorithm is shown to be higher compared to the MSE-optimal soft thresholding denoising solution, as measured by the SSIM Index.