This paper presents crystal-MUSIC, a method for DOA estimation of multiple sources in the presence of diffuse noise. MUSIC is well known as a method for the estimation of the DOAs of multiple sources but is not very robust to diffuse noise from many directions, because the covariance structure of such noise is not spherical. Our method makes it possible for MUSIC to accurately estimate the DOAs by removing the contribution of diffuse noise from the spatial covariance matrix. The denoising of the matrix (i.e. removal of the diffuse noise component) consists of two steps: 1) denoising of the off-diagonal entries via a blind noise decorrelation using crystal-shaped arrays, and 2) denoising of the diagonal entries through a low-rank matrix completion technique. The denoising process does not require the spatial covariance matrix of diffuse noise to be known, but relies only on an isotropy feature of diffuse noise. Experimental results with real-world noise show that the DOA estimation accuracy is substantially improved compared to the conventional MUSIC.