A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, July 14, 2015. / Hyperspectral images nd application in many areas of modern society, we use them for land surveying, core sample analysis, in the conservation and forestry industries and many more. A major problem in hyperspectral images is how to deal with noise. Many methods that analyse hyperspectral images either need clean images or accurate estimations of the noise statistics in the images. The goal of this dissertation is to present and compare methods for statistic estimation and noise removal. We use an arti cial hyperspectral image to study some existing methods and develop some new ones based on existing methods, speci cally the BM3D algorithm. We test methods that estimate the level of the noise present in an image, methods that estimate the structure of the noise and methods that remove noise. We analyse all the methods under an additive noise model and consider spectrally correlated and uncorrelated noise. Within our investigations we investigate di erent types of correlation. We will show the strengths that the various methods have and establish a way to approach treating a hyperspectral image with no information beyond the image itself. Using our observations and insights from the experiments on the arti cial data we analyse some radiance data from the AVIRIS instrument. We show that the additive signal independent part of the noise is small but not negligible. We also show some evidence for the structure of the noise in the AVIRIS instrument.