Abstract: Two shearlet-based denoising methods using trivariate prior model are proposed for image denoising. The dependency among shearlet coefficients is analyzed via mutual information. According to the dependency characterization, a noisy coefficient s, its parent coefficient p and its cousin coefficient c with opposite orientation are exploited to establish the trivariate maximum a posteriori estimate model. In the case of s, p, c having the same standard deviation, a simple closed-form solution is derived from the trivariate model. For s, p, c with different standard deviations, an iterative denoising method is given, and the convergence of the iterative algorithm is proved. Experimental results show that the denoised images by the proposed methods achieve not only better visual quality but also higher peak signal-to-noise ratio (PSNR) and mean structural similarity (MSSIM) values.