Abstract
In this paper, we provide a simplified understanding of the guarantees of 1-dimension total variation minimization. We consider a slightly modified total variation minimization rather than the original one. The modified model can be transformed into an \( \ell_{1} \) minimization problem by several provable mathematical tools. With the techniques developed in random sampling theory, some estimates relative to Gaussian mean width are provided for both Gaussian and sub-Gaussian sampling. We also present a sufficient condition for the exact recovery under Gaussian sampling.
This research is partly supported by the National High Technology Research and Development Program of China (No. 2012AA01A301), National Natural Science Foundation of China (No. 61402495, No. 61170046, No.11401580, No. 61402496, No. 61303189, No.61170049), Science Project of National University of Defense Technology (JC120201) and National Natural Science Foundation of Hunan Province in China (13JJ2001).
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Jiang, H., Sun, T., Du, PB., Li, SG., Li, CJ., Cheng, LZ. (2016). A Note on the Guarantees of Total Variation Minimization. In: Huang, DS., Jo, KH. (eds) Intelligent Computing Theories and Application. ICIC 2016. Lecture Notes in Computer Science(), vol 9772. Springer, Cham. https://doi.org/10.1007/978-3-319-42294-7_19
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DOI: https://doi.org/10.1007/978-3-319-42294-7_19
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