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Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: Experimental results reveal that the proposed Hadamard-based random projection with the fast SVD (FSVD) offers a computationally attractive alternative to not only traditional SVD but also Gaussian-based FSVD for dimensionality reduction in hyperspectral classification.
Abstract: While data-dependent dimensionality reduction has dominated in many applications of hyperspectral imagery, there is increasing interest in data-independent strategies—such as random projections—due to their promise for reduced computational complexity as well as their demonstrated ability to preserve application-important information. Such random-projection-based dimensionality reduction is investigated in the specific context of supervised hyperspectral classification. Both Hadamard- and Gaussian-based random projections are considered, applied alone as well as incorporated into a fast approximate singular value decomposition (SVD). Experimental results reveal that the proposed Hadamard-based random projection with the fast SVD (FSVD) offers a computationally attractive alternative to not only traditional SVD but also Gaussian-based FSVD for dimensionality reduction in hyperspectral classification.
26 citations
TL;DR: In a Hadamard manifold with sectional curvature bounded from below by −k22, this article gave sharp upper estimates for the difference circumradius minus inradius of a compact k 2-convex domain, and also estimated the quotient (Total d-mean curvature)/area of a convex domain.
Abstract: In a Hadamard manifold with sectional curvaturebounded from below by −k22, we give sharp upper estimates for the difference circumradius minus inradiusof a compact k2-convex domain, and we getalso estimates for the quotient (Total d-mean curvature)/Area of a convex domain.
26 citations
TL;DR: In this article, an instrument combining fluorescence microscopy with Hadamard transform multiplexed imaging was designed by which a three-dimensional HadAMT fluorescence microscopic cell image was obtained.
25 citations
TL;DR: Phylogenetic spectral analysis based on Hadamard transforms is used to interconvert between an underlying evolutionary model and the ex?
Abstract: Phylogenetic spectral analysis based on Hadamard transforms is an interesting new development for the inference of evo? lutionary trees and for understanding the interrelationships of existing methods (Hendy and Penny, 1989, 1993; Steel et al., 1993a; Hendy et al., 1994; Lento et al., 1994). We use it to interconvert between an underlying evolutionary model and the ex? pected frequencies of patterns observed in sequences. Because the Hadamard is a dis? crete Fourier transform on a finite group (Diaconis, 1988), we call this approach spectral analysis. It gives a mathematical description of an invertible relationship be? tween data and model: the expected fre? quencies of patterns in the data can be cal? culated from the model, and the model can be recovered consistently from the fre? quencies of patterns in the data. Recently, Takezaki and Nei (1994) que? ried four aspects of the utility of spectral analysis: the use of the parsimony criterion after correcting for multiple changes (cor? rected parsimony), the current limitation of spectral analysis on nucleotide sequenc? es to the Kimura 3-ST mechanism of evo? lution, the relationship between a Hada? mard transform and the minimum
25 citations
TL;DR: Hadamard transform spectrometry (HTS) provides a means of obtaining a multiplex advantage with a dispersive spectrometric technique Two recent advances, stationary electro-optic encoding masks and efficient spectrum-recovery techniques to compensate for nonidealities in the masks, have combined to revive interest in HTS as mentioned in this paper.
25 citations