Hyperspectral images (HSIs) are often degraded by different noise types such as Gaussian and sparse noise. In this project proposes, a hyperspectral mixed Gaussian and sparse noise reduction technique, the HyMiNoR, is proposed. The proposed technique, hierarchically, removes the mixed noise. First, the Gaussian noise is removed using a recently developed automatic hyperspectral noise removal technique called hyperspectral restoration (HyRes). Then, we develop a novel sparse noise removal technique to remove the sparse noise, including salt and pepper noise, missing pixels, and missing lines. The performance of the proposed approach has been validated using both real and simulated data sets. Results on the simulated data set confirm considerable improvements in terms of signal-to-noise ratio and singular angle distance compared to the state of the art techniques used in the experiments. In addition, visual improvements can be clearly observed in the case of real data set experiments. This project is implemented with MATLAB software.