Recently developed Dual Domain Image Denoising (DDID) algorithm is a simple version of block-matching 3D filtering (BM3D) by combining bilateral filter and frequency-based method. DDID and its invariants have achieved competitive results compared with state-of-the-art methods. However, this kind of methods share a common drawback: there are a few parameters of the algorithms that are data- and noise-dependent, and difficult to tune. In this paper, we propose to use Stein's unbiased risk estimate (SURE) to measure the mean square error (MSE) of the DDID algorithm for restoration of an image contaminated with additive white Gaussian noise. We derive an explicit expression for SURE value to optimize parameters without access to the noise-free signal. Experimental results demonstrate the effectiveness of the proposed parameter selection in term of both quantitative and qualitative metrics.