20 April 2016 Reconstruction of sparse data generated by repeated data-based decomposition
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Abstract
The l1-norm reconstruction techniques have enabled exact data reconstruction with high probability from 'k-sparse' data. This paper presents an added technique to press this reconstruction by truncating the data in its decomposed state. The truncation utilizes a transformation of the eigen-vectors of the covariance matrix and prioritizes the vectors equally without regard to their energy levels associated to the eigenvalues of the vectors. This method presents two primary advantages in data representation: first, the data is naturally represented in only a few terms, components of each of the vectors, and second, the complete set of features is represented, albeit, the fidelity of the representation may have changed. This investigation provides a means of dealing with issues associated with high-energy fading of small-signal data features. One may think of the current technique as a method to inject sparsity into the data that is methodical with consideration of key features represented in eigen-vectors of the covariance matrix of the data.
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Vahid R. Riasati, Vahid R. Riasati, } "Reconstruction of sparse data generated by repeated data-based decomposition", Proc. SPIE 9845, Optical Pattern Recognition XXVII, 98450L (20 April 2016); doi: 10.1117/12.2225034; https://doi.org/10.1117/12.2225034
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