Simultaneous Denoising and Intrinsic Order Selection in Hyperspectral Imaging

In this paper, we address the problem of order selection in noisy hyperspectral applications. In conventional unmixing methods, this problem has been divided into two separate processes of order selection and unmixing. Order selection methods generally use a denoising approach at the beginning stage. The data in this case pass through three stages: denoising, order selection, and unmixing. Each of these steps mainly aims to optimize a different criterion independently. In addition, any error created in the denoising process will be propagated not only to the order selection stage but also consequently to the unmixing results. Commonly used denoising methods such as eigenvalue-decomposition-based methods, e.g., singular-value-decomposition-based methods, provide a threshold value to separate the noise from the signal. These approaches are heavily sensitive to the threshold value and signal-to-noise ratio (SNR). Moreover, these methods tend to lose their efficiency rapidly for lower SNRs. Note that both the denoising step and the dimension estimation step aim to provide the optimum estimate of the same noiseless data. Consequently, adopting a simultaneous denoising and dimension estimation method with a goal to provide the optimum estimate of the desired noiseless data is rational. This process not only avoids possible error propagations from the denoising stage to the dimension estimation stage but also unifies the optimization criteria that were used in each of these steps. In this paper, a simultaneous denoising and dimension estimation method is introduced. The approach is based on minimizing the estimated mean square error. Minimization is done by comparing the estimated data in a range of subspaces dictated by a simultaneous process. Minimizing the error at once, the proposed method denoises the data and provides the optimum dimension simultaneously. Owing to the parallel processing of denoising and dimension estimation, the simulation results show the advantages of the proposed method over some of the state-of-the-art approaches and illustrate a substantial performance, particularly for cases with a lower SNR.