Abundance fully constrained least squares (FLCS) method has been widely used for spectral unmixing. A modified
FCLS (MFCLS) was previously proposed for the same purpose to derive two iterative equations for solving fully
abundance-constrained spectral unmixing problems. Unfortunately, its advantages have not been recognized. This paper conducts a comparative study and analysis between FCLS and MFCLS via custom-designed synthetic images and real images to demonstrate that while both methods perform comparably in unmixing data, MFCLS edges out FCLS in less computing time.
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.
Since Magnetic Resonance (MR) images can be considered as multispectral images where each spectral band image is
acquired by a particular pulse sequence, this paper investigates an application of a technique that is widely used in
multispectral image processing, referred to as Linear Spectral Unmixing (LSU), in MR image analysis where two types
of LSU, unconstrained LSU and constrained LSU are considered. Due to a limited number of MR images acquired by
MR sequences, the ability of the LSU cannot be fully explored and utilized. In order to mitigate this dilemma, a band
expansion process is introduced to expand an original set of MR images to an augmented set of multsipectral images by
including additional spectral band images that can be generated from the original MR images using a set of nonlinear
functions. In order to demonstrate the utility of the LSU in MR image analysis, two sets of MR images, synthetic MR
images available on website and real MR images, are used for experiments. Experimental results show that the LSU can
be a very effective technique in quantifying MR substances to calculate their partial volumes for further MR image
analysis.
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