Many hyperspectral image processing algorithms (e. g., detection, classification, endmember extraction, and so on) are generally designed with the assumption of no spectral or spatial correlation in noise. However, previous studies have shown the presence of nonnegligible correlation between the noise samples in different spectral bands, especially between noises in adjacent bands, and that most of the well-known intrinsic dimension estimation algorithms give poor estimates in the presence of correlated noise. Thus, there is a need to tackle the specific case of spectrally correlated noise for noise estimation. We show, in this paper, that the commonly employed hyperspectral noise estimation algorithm based on regression residuals can be significantly affected by spectrally correlated noise and we suggest a modified approach that proves to be robust to noise correlation. Furthermore, the proposed method improves the noise variance estimates in comparison to the classic residual method even for the case of uncorrelated noise. Simulation results show that the estimation error is reduced at times by a factor of 5 when there is high spectral correlation in the noise. Our proposed per-pixel noise estimator requires an estimate of the noise covariance matrix, and for this, we also propose a method to estimate the noise covariance matrix. Simulation results demonstrate that the per-pixel noise estimates obtained via the use of estimated noise statistics are almost as good as those obtained via use of the true statistics.