Progressive dimensionality reduction by transform for hyperspectral imagery

摘要

This paper develops to a new concept, called progressive dimensionality reduction by transform (PDRT), which is particularly designed to perform data dimensionality reduction in terms of progressive information preservation. In order to materialize the PRDT a key issue is to prioritize information contained in each spectral-transformed component so that all the spectral transformed components will be ranked in accordance with their information priorities. In doing so, projection pursuit (PP)-based dimensionality reduction by transform (DRT) techniques are developed for this purpose where the Projection Index (PI) is used to define the direction of interestingness of a PP-transformed component, referred to as projection index component (PIC). The information contained in a PIC is then calculated by the PI and used as the priority score of this particular PIC. Such a resultant PDRT is called progressive dimensionality reduction by projection index-based projection pursuit (PDR-PIPP) which performs PDRT by retaining an appropriate set of PICs for information preservation according to their priorities. Two procedures are further developed to carry out PDR-PIPP in a forward or a backward manner, referred to forward PDR-PIPP (FPDR-PIPP) or backward PDRT (BPDR-PIPP), respectively, where FPDR-PIPP can be considered as progressive band expansion by starting with a minimum number of PICs and adding new PICs progressively according to their reduced priorities as opposed to BPDRT which can be regarded progressive band reduction by beginning with a maximum number of PICs and removing PICs with least priorities progressively. Both procedures are terminated when a stopping rule is satisfied. The advantages of PDR-PIPP allow users to transmit, communicate, process and store data more efficiently and effectively in the sense of retaining data integrity progressively.