Abstract:Energy transfer between the interacting waves in a distributed Brillouin sensor can result in a distorted measurement of the local Brillouin gain spectrum, leading to systematic errors. It is demonstrated that this depletion effect can be precisely modelled. This has been validated by experimental tests in an excellent quantitative agreement. Strict guidelines can be enunciated from the model to make the impact of depletion negligible, for any type and any length of fiber. Gonzalez-Herraez, "Brillouin optical time-domain analysis assisted by second-order Raman amplification," Opt. Express 18(18), 18769-18778 (2010). 13. Y. Dong, L. Chen, and X. Bao, "System optimization of a long-range Brillouin-loss-based distributed fiber sensor," Appl. Opt. 49(27), 5020-5025 (2010). 14. M. Niklès, L. Thévenaz, and P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21(10), 758-760 (1996). 15. S. Diaz, S. Mafang-Foaleng, M. Lopez-Amo, and L. Thevenaz, "A high-performance optical time-domain Brillouin distributed fiber sensor," IEEE Sens. J. 8(7), 1268-1272 (2008

We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect to variants of norms, under a capacity assumption on the hypothesis space and a regularity condition on the target function. As a result, we obtain optimal rates for regularized algorithms with randomized sketches, provided that the sketch dimension is proportional to the effective dimension up to a logarithmic factor. As a byproduct, we obtain similar results for Nyström regularized algorithms. Our results provide optimal, distribution-dependent rates that do not have any saturation effect for sketched/Nyström regularized algorithms, considering both the attainable and non-attainable cases.

CEIs/ARBs therapy might be associated with a reduce risk of CRC development, but whether use of these medications improves the outcomes of CRC remains unknown. Large-scale and more robust studies are needed to further explore this association.

The energy transfer between the two interacting optical waves in a distributed sensor based on stimulated Brillouin scattering can lead to a non-uniform spectral distribution of the pumping power after a long propagation. This results in a spectrally distorted gain that biases the determination of the maximum gain frequency. A quantitative analytical model gives an expression for the tolerable pump power change keeping the maximum bias within a given accuracy.

This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly constrained l 1 -analysis optimization problem, called analysis Dantzig selector, stably recovers a signal which is nearly sparse in terms of a tight frame provided that the measurement matrix satisfies a restricted isometry property adapted to the tight frame. As a special case, we consider the Gaussian noise. Further, under a sparsity scenario, with high probability, the recovery error from noisy data is within a log-like factor of the minimax risk over the class of vectors which are at most s sparse in terms of the tight frame. Similar results for the analysis LASSO are shown.The above two algorithms provide guarantees only for noise that is bounded or bounded with high probability (for example, Gaussian noise). However, when the underlying measurements are corrupted by sparse noise, these algorithms perform suboptimally. We demonstrate robust methods for reconstructing signals that are nearly sparse in terms of a tight frame in the presence of bounded noise combined with sparse noise. The analysis in this paper is based on the restricted isometry property adapted to a tight frame, which is a natural extension to the standard restricted isometry property.