With the current state-of-the-art computer aided manufacturing tools, the spatial resolution of hyperspectral sensors is becoming increasingly higher thus making it easy to obtain much more detailed information of the scene captured. However, the improvement of the spatial resolution also brings new challenging problems to address with signal dependent photon noise being one of them. Unlike the signal independent thermal noise, the variance of photon noise is dependent on the signal, therefore many denoising methods developed for the stationary noise cannot be applied directly to the photon noise. To make things worse, both photon and thermal noise coexist in the captured hyperspectral image (HSI), thus making it more difficult to whiten noise. In this paper, we propose a new denoising framework to cope with signal dependent nonwhite noise (SDNW), Pre-estimate—Whitening—Post-estimate (PWP) loop, to reduce both photon and thermal noise in HSI. Previously, we proposed a method based on multidimensional wavelet packet transform and multi-way Wiener filter which performs both white noise and spectral dimensionality reduction, referred to as MWPT-MWF, which was restricted to white noise. We get inspired from this MWPT-MWF to develop a new iterative method for reducing photon and thermal noise. Firstly, the hyperspectral noise parameters estimation (HYNPE) algorithm is used to estimate the noise parameters, the SD noise is converted to an additive white Gaussian noise by pre-whitening procedure and then the whitened HSI is denoised by the proposed method SDNW-MWPT-MWF. As comparative experiments, the Multiple Linear Regression (MLR) based denoising method and tensor-based Multiway Wiener Filter (MWF) are also used in the denoising framework. An HSI captured by Reflective Optics System Imaging Spectrometer (ROSIS) is used in the experiments and the denoising performances are assessed from various aspects: the noise whitening performance, the Signal-to-Noise Ratio (SNR), and the classification performance. The results on the real-world airborne hyperspectral image HYDICE (Hyperspectral Digital Imagery Collection Experiment) are also presented and analyzed. These experiments show that it is worth taking into account noise signal-dependency hypothesis for processing HYDICE and ROSIS HSIs.