A Variational Approach for Denoising Hyperspectral Images Corrupted by Poisson Distributed Noise Ferdinand Deger 1,2 , Alamin Mansouri 1 , Marius Pedersen 2 , Jon Yngve Hardeberg 2 , and Yvon Voisin 1 1 Le2i – Universit´ e de Bourgogne, Auxerre, France ferdinand.deger@u-bourgogne.fr 2 Norwegian Colour and Visual Computing Laboratory – Gjøvik University College, Gjøvik, Norway Abstract. Poisson distributed noise, such as photon noise is an impor- tant noise source in multi- and hyperspectral images. We propose a vari- ational based denoising approach, that accounts the vectorial structure of a spectral image cube, as well as the poisson distributed noise. For this aim, we extend an approach for monochromatic images, by a regularisa- tion term, that is spectrally and spatially adaptive and preserves edges. In order to take the high computational complexity into account, we de- rive a Split Bregman optimisation for the proposed model. The results show the advantages of the proposed approach compared to a marginal approach on synthetic and real data. 1 Introduction Multi- and Hyperspectral imaging (HSI) combine digital imaging and spec- troscopy, and has numerous applications in remote sensing, mineralogy, cultural heritage documentation etc. The technology acquires radiometric information for every pixel in an image. The discrete number of spectral bands form, in combination with the spatial information a 3-dimensional data cube. Spectral images contain noise, which impacts the precision of further process- ing steps, such as unmixing, classification, reflectance estimation [10] or compres- sion [4]. The image noise includes signal-dependent components, such as photon noise, and signal-independent components such as dark noise or fixed pattern noise. Previous research [1,7,12] identified the photon noise, as the most relevant noise contribution in HSI. Hyperspectral scanners are sophisticated, individually calibrated devices with a high signal to noise ratio (SNR). Signal-dependent noise components are proportional to the signal amplitude, and are therefore more im- portant in images with a high SNR [12]. HSI applications, outside the field of remote sensing allow to repeat a single measurement multiple times, and increase the SNR further [1]. Calibrated scanners allow a compensation for the relative responsivity of detector elements and therefore suppress fixed noise patterns [9]. Common applications have a low number of photons, due to a weak signal or a large distance, which leads to a photon-limited regime [7]. A. Elmoataz et al. (Eds.): ICISP 2014, LNCS 8509, pp. 106–114, 2014. c  Springer International Publishing Switzerland 2014