ADMM based Hyperspectral Image Classification Improved by Denoising using Legendre Fenchel Transformation

This paper discusses about a sparsity based algorithm used for Hyperspectral Image (HSI) classification where the test pixel vectors are sparsely represented as the linear combination of a few number of training samples from a well-organised dictionary matrix. The sparse vector is obtained using Basis Pursuit (BP) which is a constrained l4 minimization problem. This problem is solved by using a simple and powerful iterative algorithm known as Alternating Direction Method of Multipliers (ADMM) which significantly reduces the computational complexity of the problem and thereby speeds up the convergence. The classification accuracy is considerably improved by including efficient preprocessing techniques to remove the unwanted information (noise) present in Hyperspectral images. This paper uses a fast and reliable denoising technique based on Legendre Fenchel Transformation (LFT) to effectively denoise each band of HSI prior to ADMM based classification (proposed method). A comparison of proposed technique with one of the convex optimization tools namely, CVX is given to exhibit the fast convergence of the former method. The experiment is performed on standard Indian Pines dataset captured using AVIRIS sensor. The potential of the proposed method is illustrated by analyzing the classification indices obtained with and without applying any preprocessing methods. With only 10% training set, an overall accuracy of 96.76% is obtained for the proposed method at a much faster rate compared to computation time taken by CVX solver.