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Abstract: Image fusion can produce a single image that describes the scene better than the individual source image. One of the keys to image fusion algorithm is how to effectively and completely represent the source images. Morphological component analysis (MCA) believes that an image contains structures with different spatial morphologies and can be accordingly modeled as a superposition of cartoon and texture components, and that the sparse representations of these components can be obtained by some specific decomposition algorithms which exploit the structured dictionary. Compared with the traditional multiscale decomposition, which has been successfully applied to pixel-level image fusion, MCA employs the morphological diversity of an image and provides more complete representation for an image. Taking advantage of this property, we propose a multi-component fusion method for multi-source images in this paper. In our method, source images are separated into cartoon and texture components, and essential fusion takes place on the representation coefficients of these two components. Our fusion scheme is verified on three kinds of images and compared with six single-component fusion methods. According to the visual perceptions and objective evaluations on the fused results, our method can produce better fused images in our experiments, compared with other single-component fusion methods. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the Cholesky decomposition of the Hermitian positive definite quaternion matrix. For the first time, the structure-preserving Gauss transformation is defined, and then a novel structure-preserving algorithm, which is applied to its real representation matrix, is proposed. Our algorithm needs only real number operations, does not depend on the quaternion toolbox for matlab (QTFM) and has more portability. Although the flops of our algorithm are theoretically about the same as those based on quaternion arithmetic operations or QTFM, numerical experiments show that our algorithm runs faster. [Copyright &y& Elsevier]

Abstract: An essential task in comparative genomics is to decompose two or more genomes into synteny blocks that are segments of chromosomes with similar contents. Given a set of genomic maps each containing the same markers without duplicates, the problem Maximal Strip Recovery (MSR) aims at finding a decomposition of the genomic maps into synteny blocks (strips) of the maximum total length , by deleting the minimum number of markers which are probably noise and ambiguities. In this paper, we present a collection of new or improved FPT and approximation algorithms for MSR and its variants. Our main results include a time FPT algorithm for -gap-MSR-, a time FPT algorithm for both CMSR- and -gap-CMSR-, and a -approximation algorithm for both CMSR- and -gap-CMSR-. [Copyright &y& Elsevier]