FastVGBS: A Fast Version of the Volume-Gradient-Based Band Selection Method for Hyperspectral Imagery

Recently, the volume-gradient-based band selection (VGBS) method has attracted more and more attention in the field of band selection. It is a ranking-based unsupervised algorithm which applies the sequential backward selection strategy to successively remove the most abundant band. The key finding of VGBS is that the band redundancy corresponds to the volume gradient matrix with respect to hyperspectral images. However, we have found that VGBS requires to update the gradient matrix after each band removal, which includes the calculation of the matrix inverse, determinant, and multiplication, and thus is time-consuming when the number of bands is large. In this letter, we first find that the norm of the row of the gradient matrix has a one-to-one correspondence to the diagonal element of the covariance matrix of the image. Further, we develop a recursive formula to calculate the inverse of the covariance matrix. The experimental results show the effectiveness of the method, i.e., we can reduce the computational complexity of VGBS with an order of magnitude.