We propose a framework for the denoising of videos jointly corrupted by spatially correlated (i.e., nonwhite) random noise and spatially correlated fixed-pattern noise. Our approach is based on motion-compensated 3D spatiotemporal volumes, i.e., a sequence of 2D square patches extracted along the motion trajectories of the noisy video. First, the spatial and temporal correlations within each volume are leveraged to sparsify the data in 3D spatiotemporal transform domain, and then the coefficients of the 3D volume spectrum are shrunk using an adaptive 3D threshold array. Such array depends on the particular motion trajectory of the volume, the individual power spectral densities of the random and fixed-pattern noise, and also the noise variances which are adaptively estimated in transform domain. Experimental results on both synthetically corrupted data and real infrared videos demonstrate a superior suppression of the random and fixed-pattern noise from both an objective and a subjective point of view.