Hyperspectral Image Classification with Spatial Filtering and \(l_{(2,1)}\) Norm

Abstract

Recently, the sparse representation based classification methods have received particular attention in the classification of hyperspectral imagery. However, current sparse representation based classification models have not considered all the test pixels simultaneously. In this paper, we propose a hyperspectral classification method with spatial filtering and ℓ2,1 norm (SFL) that can deal with all the test pixels simultaneously. The ℓ2,1 norm regularization is used to extract relevant training samples among the whole training data set with joint sparsity. In addition, the ℓ2,1 norm loss function is adopted to make it robust for samples that deviate significantly from the rest of the samples. Moreover, to take the spatial information into consideration, a spatial filtering step is implemented where all the training and testing samples are spatially averaged with its nearest neighbors. Furthermore, the non-negative constraint is added to the sparse representation matrix motivated by hyperspectral unmixing. Finally, the alternating direction method of multipliers is used to solve SFL. Experiments on real hyperspectral images demonstrate that the proposed SFL method can obtain better classification performance than some other popular classifiers.

Cone-based joint sparse modelling for hyperspectral image classification

“…We evaluate the proposed C-JSM (14) and compare it with five base- (13) and (14). The labelling by the single models is determined by (6), whereas the labelling by the joint models is determined by (8).…”

“…We call this new model (14) the cone-based joint sparse model (shortened as C-JSM). In short, the proposed C-JSM incorporates the non-negative constraints into the sparse representation of a test window X by joint modelling.…”

“…We propose a new algorithm called non-negative simultaneous orthogonal matching pursuit (NN-SOMP), to solve the C-JSM problem. It combines the NNLS-based methods and the SOMP algorithm together to produce a non-negative and sparse estimation of the coefficient matrix in (14). Before introducing the proposed NN-SOMP, we first present the non-negative OMP to get an insight of the paradigm.…”

“…Following the derivation of NN-OMP from OMP, we propose a new algorithm called NN-SOMP, which combines the SOMP algorithm [21] and the NNLS-based methods together to solve the problem of C-JSM (14).…”

“…Recently, sparse representation has been extensively investigated in hyperspectral imaging [3][4][5][6][7][8][9][10][11][12][13][14]. A hyperspectral image (HSI) is a 3-dimensional data cube with two spatial dimensions and one spectral dimension.…”