Keng-Hao Liu

Kernel-Based Linear Spectral Mixture Analysis

Linear spectral mixture analysis (LSMA) has been widely used in remote sensing community for spectral unmixing. This letter develops a promising technique, called kernel-based LSMA (KLSMA), which uses nonlinear kernels to resolve the issue of nonlinear separability arising in unmixing and further extends several commonly used LSMA techniques to their kernel-based counterparts. Interestingly, according to experiments conducted for real hyperspectral and multispectral images, KLSMA is more effective than LSMA when data samples are heavily mixed.

Kernel-based Linear Spectral Mixture Analysis for hyperspectral image classification

Linear Spectral Mixture Analysis (LSMA) has been widely used in remote sensing community. Recently, kernel-based approaches have received considerable interest in hyperspectral image analysis where nonlinear kernels are used to resolve the issue of nonlinear separability in classification. This paper extends the LSMA to kernel-based LSMA where three least squares-based LSMA techniques, least squares orthogonal subspace projection (LSOSP), non-negativity constrained least squares (NCLS) and fully constrained least squares (FCLS) are extended to their kernel counterparts, KLSOSP, KNCLS and KFCLS.

Progressive Band Processing of Linear Spectral Unmixing for Hyperspectral Imagery

This paper develops a new approach, called progressive band processing (PBP) of linear spectral unmixing (LSU) which can process data unmixing according to band sequential (BSQ) format. This new concept is quite different from band selection (BS) which must select bands from a fully collected band set based on a band optimization criterion. There are several advantages of using PBP-LSU over BS. In particular, it allows users to perform LSU using available bands without waiting for a complete collection of full bands. In doing so, an innovations information update equation is further derived and can process LSU as its band process is ongoing. To be more specific, LSU can be carried out by PBP by updating unmixed data recursively band by band in the same way that a Kalman filter does for updating data information in a recursive fashion. With such a recursion in nature, PBP is able to process bands of interest which may vary with different applications.

Real-time progressive band processing of Modified Fully Abundance-Constrained Spectral Unmixing

Band selection (BS) has advantages over data dimensionality in satellite communication and data transmission. However, several issues regarding real time processing need to be addressed, (1) how many bands required for BS, (2) how to select appropriate bands, (3) how to take advantage of previously selected bands without re-implementing BS, and finally and most important, (4) how to tune bands to be selected in real time as number of bands varies. This paper presents a new approach, called progressive band processing (PBP) for Modified Fully Abundance-Constrained Spectral Unmixing (MFCLS) without actually implementing BS. When spectral unmixing is performed, BS must be done prior to data unmixing in which case real time implementation in data communication is infeasible. The proposed PBP-MFCLS allows users to incorporate new incoming bands into data unmixing currently being processed. Accordingly, PBP-MFCLS can be carried out band by band in a real time and progressive fashion with unmixed data updated recursively band by band in the same way that data is processed by a Kalman filter.

Kernel-Based Weighted Abundance Constrained Linear Spectral Mixture Analysis for Remotely Sensed Images

Linear spectral mixture analysis (LSMA) is a theory that can be used to perform spectral unmixing where three major LSMA techniques, least squares orthogonal subspace projection (LSOSP), non-negativity constrained least squares (NCLS) and fully constrained least squares (FCLS) have been developed for this purpose. Subsequently, these three techniques were further extended to Fishers LSMA (FLSMA), weighted abundance constrained LSMA (WAC-LSMA) and kernel-based LSMA (K-LSMA). This paper combines both approaches of KLSMA and WAC-LSMA to derive a most general version of LSMA, kernel-based WACLSMA (KWAC-LSMA), which includes all the above-mentioned LSMA as its special cases. In particular, a new version of kernelizing FLSMA, referred to as kernel FLSMA (K-FLSMA) can be also developed to enhance the FLSMA performance by replacing the weighting matrix used in WAC-LSMA with a matrix specified by the within-class scatter matrix. The utility of the KWAC-LSMA is further demonstrated by multispectral and hyperspectral experiments for performance analysis.

Dynamic band selection for hyperspectral imagery

This paper presents a new BS, called dynamic BS (DBS) which revolutionizes the commonly used BS by considering the number of bands to be selected, p as a variable which varies with criterion used for BS and different applications. Its idea is derived from information theory where it assumes that signal sources are considered as source alphabets with probabilities being their mutual spectral discriminatory powers calculated by a spectral similarity measure. If we further assume that a signal source is accommodated by a particular spectral band, the signal source will be encoded by 1 indicating a band being used to specify the signal source and 0 otherwise. Accordingly, band dimensionality to discriminate a signal source from other sources can be determined by its variable coding length obtained by the Huffman coding. With this interpretation the conventional BS can be considered as a fixed-dimensionality BS, referred to as static BS(SBS).

Progressive Dimensionality Reduction for Hyperspectral Imagery

This paper develops to a new concept, called Progressive Dimensionality Reduction (PDR) which can perform data dimensionality progressive in terms of information preservation. Two procedures can be designed to perform PDR in a forward or backward manner, referred to forward PDR (FPDR) or backward PDR (BPDR) respectively where FPDR starts with a minimum number of spectral-transformed dimensions and increases the spectral-transformed dimension progressively as opposed to BPDR begins with a maximum number of spectral-transformed dimensions and decreases the spectral-transformed dimension progressively. Both procedures are terminated when a stopping rule is satisfied. In order to carry out DR in a progressive manner, DR must be prioritized in accordance with significance of information so that the information after DR can be either increased progressively by FPDR or decreased progressively by BPDR. To accomplish this task, Projection Pursuit (PP)-based DR techniques are further developed where the Projection Index (PI) designed to find a direction of interestingness is used to prioritize directions of Projection Index Components (PICs) so that the DR can be performed by retaining PICs with high priorities via FPDR or BPDR. In the context of PDR, two well-known component analysis techniques, Principal Components Analysis (PCA) and Independent Component Analysis (ICA) can be considered as its special cases when they are used for DR.

Exploration of component analysis in multi/hyperspectral image processing

Component Analysis (CA) has found many applications in remote sensing image processing. Two major component analyses are of particular interest, Principal Components Analysis (PCA) and Independent Component Analysis (ICA) which have been widely used in signal processing. While the PCA de-correlates data samples via 2nd order statistics in a set of Principal Components (PCs), the ICA represents data samples via statistical independency in a set of statistically Independent Components (ICs). However, in order to for component analyses to be effective, the number of components to be generated, p must be sufficient for data analysis. Unfortunately, in MultiSpectral Imagery (MSI) p seems to be small, while p in HyperSpectral Imagery (HSI) seems too large. Interestingly, very little has been reported on how to deal with this issue when p is too small or too large. This paper investigates this issue. When p is too small, two approaches are developed to mitigate the problem. One is Band Expansion Process (BEP) which augments original data band dimensionality by producing additional bands via a set of nonlinear functions. The other is a kernel-based approach, referred to as Kernel-based PCA (K-PCA) which maps features in the original data space to a higher dimensional feature space via a set of nonlinear kernel. While both approaches make attempts to resolve the issue of a small p using a set of nonlinear functions, their design rationales are completely different, particularly they are not correlated. As for a large p such as HSI, a recently developed Virtual Dimensionality (VD) can be used for this purpose where the VD was originally developed to estimate number of spectrally distinct signatures. If we assume one spectrally distinct signature can be accommodated by one component, the value of p can be actually determined by the VD. Finally, experiments are conducted to explore and evaluate the utility of component analyses, specifically, PCA and ICA using BEP and K-PCA for MSI and VD for HSI.

Real-time progressive band processing of linear spectral unmixing

Band selection (BS) has advantages over data dimensionality in satellite communication and data transmission in the sense that the spectral bands can be tuned by users at their discretion for data analysis while keeping data integrity. However, to materialize BS in such practical applications several issues need to be addressed. One is how many bands required for BS. Another is how to select appropriate bands. A third one is how to take advantage of previously selected bands without re-implementing BS. Finally and most importantly is how to tune bands to be selected in real time as number of bands varies. This paper presents an application in spectral unmixing, progressive band selection in linear spectral unmixing to address the above-mentioned issues where data unmixing can be carried out in a real time and progressive fashion with data updated recursively band by band in the same way that data is processed by a Kalman filter.

Kernel-based weighted abundance constrained linear spectral mixture analysis

Linear Spectral Mixture Analysis (LSMA) is a theory developed to perform spectral unmixing where three major LSMA techniques, Least Squares Orthogonal Subspace Projection (LSOSP), Non-negativity Constrained Least Squares (NCLS) and Fully Constrained Least Squares (FCLS) for this purpose. Later on these three techniques were further extended to Fishers LSMA (FLSMA), Weighted Abundance Constrained-LSMA (WAC-LSMA) and kernel-based LSMA (KLSMA). This paper combines both approaches of KLSMA and WACLSMA to derive a most general version of LSMA, Kernel-based WACLSMA (KWAC-LSMA) which includes all the above-mentioned LSMAs as its special cases. The utility of the KWAC-LSMA is further demonstrated by multispectral and hyperspectral experiments for performance analysis.