Band selection (BS) is one of the most important topics in hyperspectral image (HSI) processing. The objective of BS is to find a set of representative bands that can represent the whole image with lower inter-band redundancy. Many types of BS algorithms were proposed in the past. However, most of them can be carried on in an off-line manner. It means that they can only be implemented on the pre-collected data. Those off-line based methods are sometime useless for those applications that are timeliness, particular in disaster prevention and target detection. To tackle this issue, a new concept, called progressive sample processing (PSP), was proposed recently. The PSP is an "on-line" framework where the specific type of algorithm can process the currently collected data during the data transmission under band-interleavedby-sample/pixel (BIS/BIP) protocol. This paper proposes an online BS method that integrates a sparse-based BS into PSP framework, called PSP-BS. In PSP-BS, the BS can be carried out by updating BS result recursively pixel by pixel in the same way that a Kalman filter does for updating data information in a recursive fashion. The sparse regression is solved by orthogonal matching pursuit (OMP) algorithm, and the recursive equations of PSP-BS are derived by using matrix decomposition. The experiments conducted on a real hyperspectral image show that the PSP-BS can progressively output the BS status with very low computing time. The convergence of BS results during the transmission can be quickly achieved by using a rearranged pixel transmission sequence. This significant advantage allows BS to be implemented in a real time manner when the HSI data is transmitted pixel by pixel.
KEYWORDS: Data communications, Spectral data processing, Data processing, Thallium, Data compression, Satellite communications, Remote sensing, Image processing, Data analysis, Filtering (signal processing)
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.
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
Fisher's 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.
KEYWORDS: Principal component analysis, Photonic integrated circuits, Independent component analysis, Hyperspectral imaging, Statistical analysis, Data analysis, Image classification, Data modeling, Data processing, Data compression
Data dimensionality (DR) is generally performed by first fixing size of DR at a certain number, say p and then finding a
technique to reduce an original data space to a low dimensional data space with dimensionality specified by p. This
paper introduces a new concept of dynamic dimensionality reduction (DDR) which considers the parameter p as a
variable by varying the value of p to make p adaptive compared to the commonly used DR, referred to as static
dimensionality reduction (SDR) with the parameter p fixed at a constant value. In order to materialize the DDR another
new concept, referred to as progressive DR (PDR) is also developed so that the DR can be performed progressively to
adapt the variable size of data dimensionality determined by varying the value of p. The advantages of the DDR over
SDR are demonstrated through experiments conducted for hyperspectral image classification.
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.
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.
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