Chemical hyperspectral imaging (HSI) data is naturally high dimensional and large. There are thus inherent manual trade-offs in acquisition time, and the quality of data. Minimum Noise Fraction (MNF) developed by Green et al. [1] has been extensively studied as a method for noise removal in HSI data. It too, however entails a manual speed-accuracy trade-off, namely the process of manually selecting the relevant bands in the MNF space. This process currently takes roughly around a month's time for acquiring and pre-processing an entire TMA with acceptable signal to noise ratio. We present three approaches termed 'Fast MNF', 'Approx MNF' and 'Rand MNF' where the computational time of the algorithm is reduced, as well as the entire process of band selection is fully automated. This automated approach is shown to perform at the same level of accuracy as MNF with now large speedup factors, resulting in the same task to be accomplished in hours. The different approximations produced by the three algorithms, show the reconstruction accuracy vs storage (50×) and runtime speed (60×) trade-off. We apply the approach for automating the denoising of different tissue histology samples, in which the accuracy of classification (differentiating between the different histologic and pathologic classes) strongly depends on the SNR (signal to noise ratio) of recovered data. Therefore, we also compare the effect of the proposed denoising algorithms on classification accuracy. Since denoising HSI data is done unsupervised, we also use a metric that assesses the quality of denoising in the image domain between the noisy and denoised image in the absence of ground truth.