Sub-pixel Mapping Method based on Total Variation Minimization and Spectral Dictionary

In this paper we tackle the problem of data analysis over the higher dimensional space provided by hyperspectral images. Remote sensing data analysis is a complex task due to numerous factors such as the large spectral and spatial diversity. The latter is the key focus of attention in this paper.As a matter of fact, mixed pixels are often sources of uncertainty which affects the accuracy of several approaches whose target is to solve the sub-pixel problem. Although spectral un-mixing techniques can provide abundance fractions within mixed pixels to each class, their associated spatial distribution remains unknown. The set of techniques aimed to solve the above mentioned problem is commonly known as sub-pixel mapping (SPM); existing algorithms based on the spatial dependence assumption cannot solve these problems efficiently and cannot provide a unique configuration for the same problem. In the context of variational framework to solve inverse problems, various strategies were proposed to avoid their intrinsic ill-posedness in the form of regularization. Differently from previous approaches of literature, which apply spatial regularization individually for each class, the proposed method takes also into account spatial links among classes. In order to improve sub-pixel mapping accuracy and, consequently, enhance hyperspectral image classification, we propose a method based on a pre-constructed spectral dictionary and isotropic total variation minimization of classes within and between pixels (SMSD-ITV). Experimental results with real and simulated data sets show the attributes of using spectral dictionary with total variation as a prior model, which lead to improve sub-pixel mapping of different classes tacking into account spatial correlation between them.