Corrupted Sensing with Sub-Gaussian Measurements

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions for stable signal recovery from structured corruption with added unstructured noise. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices.Comment: To appear in Proceedings of IEEE International Symposium on Information Theory 201

On the Phase Transition of Corrupted Sensing

In \cite{FOY2014}, a sharp phase transition has been numerically observed when a constrained convex procedure is used to solve the corrupted sensing problem. In this paper, we present a theoretical analysis for this phenomenon. Specifically, we establish the threshold below which this convex procedure fails to recover signal and corruption with high probability. Together with the work in \cite{FOY2014}, we prove that a sharp phase transition occurs around the sum of the squares of spherical Gaussian widths of two tangent cones. Numerical experiments are provided to demonstrate the correctness and sharpness of our results.Comment: To appear in Proceedings of IEEE International Symposium on Information Theory 201

Advanced materials for lithium ion batteries:surface and interface chemistry

Lithium ion batteries (LIBs) are the indispensable energy storage devices in our modern society. LiFePO4, as one of the most promising cathode, are widely used in LIBs. However, impurity phases are formed in LiFePO4 during carbon coating process due to the intrinsic strong reducing atmosphere. Herein, as the first part of my work, interface chemistry of carbon coating on LiFePO4 are symmetrically investigated by advanced characterization techniques. Two distinct secondary phases are formed during carbon coating process at different condition. Moreover, secondary phase formation is controllable by changing the particle size of LiFePO4, annealing temperature, and coating atmosphere. High-quality LiFePO4 with excellent electrochemical performance is obtained by tuning the carbon coating conditions. The formation mechanisms of secondary phases are illustrated from the thermodynamic point of view, and in well agreement with experimental observation. Next, the secondary phase during LiFePO4 synthesis and carbon coating process are characterized with energy dispersive spectroscopy, Raman, and X-ray fluorescence mapping, which give clear information about the phase distribution in obtained materials. To achieve higher energy density and safety, solid state batteries (SSBs) are developed by using inflammable solid electrolyte and a lithium anode. Unfortunately, the spread of SSBs is impeded by the interface challenges of physical mismatch, chemical reaction, and space charge effect. It is therefore necessary to engineer an interface to reduce the side reactions before assembling an SSB. In this thesis, as the second part of my work, interface between Li1.3Al0.3Ti1.7 (PO4)3 (LATP) electrolyte and Li metal is stabilized with atomic layer deposition (ALD) interlayer, which restricts the Ti reduction and Li dendrite formation. The physical mismatch of LiCoO2 and current-collector is resolved with Al substrate, which results in a fast lithium transport path. There is an element mutual diffusion region between LiCoO2 and LATP electrolyte at high temperature. By introducing an interlayer, element diffusion region is significantly reduced at LiCoO2/LATP interface. A cold sintering process at low temperature is developed, compared with conventional high-temperature sintering. The obtained solid electrolyte shows an ionic conductivity close to 10-4 S cm-1, which is applicable for solid state batteries. The research on interface chemistry in solid state batteries will help to fabricate solid batteries with small interfacial resistance