In recent years, the performance of image denoising has been boosted drastically by nonlocal algorithms and sparse coding techniques. In this paper, we also take a nonlocal approach to image denoising and formulate the problem as one of collaborative LMMSE estimation from grouped image patches. We show that our optimal LMMSE solution amounts to shrinking the singular values of the matrix representation of the grouped image patches. This interpretation of our solution allows us to relate our estimation-theoretic approach to other nonlocal algorithms and sparse coding techniques in the literature. In addition, we develop an iterative algorithm to find the best LMMSE estimate. Experimental results show that our proposed denoising algorithm achieves better PSNR and subjective performance than the state of the art.