We use a perceptual distortion metric - the structural similarity (SSIM) index, to derive a new linear estimator for estimating zero-mean Gaussian sources distorted by additive white Gaussian noise (AWGN). We use this estimator in an image denoising application and compare its performance with the traditional linear least squared error (LLSE) estimator. Although images denoised using the SSIM-optimized estimator have a lower peak signal-to-noise ratio (PSNR) compared to their LLSE couterparts, the SSIM-optimized estimator clearly outperforms the LLSE estimator in terms of the visual quality of the denoised images. ©2006 IEEE.