Hyperspectral data classification via sparse representation in homotopy

Sparse representation has significant success in many fields such as signal compression and reconstruction but to the best of our knowledge, no sparse-based classification solution has been proposed in the field of remote sensing. One of the reasons is that the general optimizers are extremely slow, time consuming and needs intensive processing for l1-minimization sparse representation. In this paper, we propose a fast sparse representation using l1-minimization based on homotopy for the classification of hyperspectral data. This method is based on the observation that a test sample can be represented by train samples from a pool of large number of train samples i.e the sparse representation. Hence the sparse representation for each test sample is achieved by the linear combination of the train samples. This proposed method has the advantages that learning on the training samples is not required, both model selection and parameter estimation are not needed, and low computational load, by which a bagging algorithm is introduced to increase the classification accuracy via voting. A real hyperspectral dataset (AVIRIS 1992 Indiana´s Indian Pines image) is used to measure the performance of the proposed algorithm. We compared the accuracy results with state-of-the-art SVM and general purpose linear programming solvers. We also presented a time comparison between our approach and general LP solvers. The comparisons prove the effectiveness of the proposed approach.