Unsupervised Rate Distortion Function-Based Band Subset Selection for Hyperspectral Image Classification

Due to significant interband correlation resulting from the use of hundreds of contiguous spectral bands, band selection (BS) is one of the most widely used methods to reduce data dimensionality for band redundancy removal. A challenge for BS is how to design an effective criterion that can select bands with preserving crucial spectral information, while also avoiding selecting highly correlated bands. Information theory turns out to be one of the best means to address such issues in terms of information redundancy, specifically, the rate distortion function (RDF) of Shannon's third noisy source coding (or joint source and channel coding) theorem, which has been widely used in image compression/coding. This article presents a novel unsupervised RDF-based band subset selection (RDFBSS) for hyperspectral image classification (HSIC). To accomplish this goal, a new concept of the area under an RDF curve, ARDF similar to the area under a receiver operating characteristic (ROC), A(z) defined in hyperspectral target detection is coined and defined as a criterion for BSS. Since BSS generally requires an exhaustive search for an optimal band subset, two iterative algorithms similar to sequential (SQ) N finder (N-FINDR) and successive (SC) N-FINDR for finding endmembers, called sequential (SQ) RDFBSS and successive (SC) RDFBSS, can be also derived and coupled with A(RDF) as a criterion to find optimal band subsets. The experimental results demonstrate that RDFBSS is indeed a very effective BS method to find the best possible band subsets and also performs better than most recent BS methods.