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   https://doi.org/10.1088/1361-6420/ac64fb  

   Wang, Chao; Tao, Min; Chuah, Chen-Nee; Nagy, James; Lou, Yifei (May 2022, Inverse Problems)

   Abstract In this paper, we study the L 1 / L 2 minimization on the gradient for imaging applications. Several recent works have demonstrated that L 1 / L 2 is better than the L 1 norm when approximating the L 0 norm to promote sparsity. Consequently, we postulate that applying L 1 / L 2 on the gradient is better than the classic total variation (the L 1 norm on the gradient) to enforce the sparsity of the image gradient. Numerically, we design a specific splitting scheme, under which we can prove subsequential and global convergence for the alternating direction method of multipliers (ADMM) under certain conditions. Experimentally, we demonstrate visible improvements of L 1 / L 2 over L 1 and other nonconvex regularizations for image recovery from low-frequency measurements and two medical applications of magnetic resonance imaging and computed tomography reconstruction. Finally, we reveal some empirical evidence on the superiority of L 1 / L 2 over L 1 when recovering piecewise constant signals from low-frequency measurements to shed light on future works. 

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2. L _1-2 Regularized Logistic Regression

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   Qin, Jing; Lou, Yifei (November 2019, 2019 53rd Asilomar Conference on Signals, Systems, and Computers)
3. Direct Transformation of SiH ₄ to a Molecular L(H) ₂ Co═Si═Co(H) ₂ L Silicide Complex

   https://doi.org/10.1021/jacs.2c11569  

   Handford, Rex C.; Nguyen, Trisha T.; Teat, Simon J.; Britt, R. David; Tilley, T. Don (February 2023, Journal of the American Chemical Society)
4. On L ₁ -Embeddability of Unions of L ₁ -Embeddable Metric Spaces and of Twisted Unions of Hypercubes

   https://doi.org/10.1515/agms-2022-0145  

   Ostrovskii, Mikhail I.; Randrianantoanina, Beata (January 2022, Analysis and Geometry in Metric Spaces)

   Abstract We study properties of twisted unions of metric spaces introduced in [Johnson, Lindenstrauss, and Schechtman 1986], and in [Naor and Rabani 2017]. In particular, we prove that under certain natural mild assumptions twisted unions of L 1 -embeddable metric spaces also embed in L 1 with distortions bounded above by constants that do not depend on the metric spaces themselves, or on their size, but only on certain general parameters. This answers a question stated in [Naor 2015] and in [Naor and Rabani 2017]. In the second part of the paper we give new simple examples of metric spaces such that their every embedding into L p , 1 ≤ p < ∞, has distortion at least 3, but which are a union of two subsets, each isometrically embeddable in L p . This extends the result of [K. Makarychev and Y. Makarychev 2016] from Hilbert spaces to L p -spaces, 1 ≤ p < ∞. 

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   https://doi.org/10.1021/acs.organomet.1c00379  

   Moore, William N.; Ziller, Joseph W.; Evans, William J. (September 2021, Organometallics)