An Efficient Approach for Computing Optimal Low-Rank Regularized Inverse Matrices

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available. In this paper, we develop a new framework that uses training data, as a substitute for knowledge of the forward model, to compute an optimal low-rank regularized inverse matrix directly, allowing for very fast computation of a regularized solution. We consider a statistical framework based on Bayes and empirical Bayes risk minimization to analyze theoretical properties of the problem. We propose an efficient rank update approach for computing an optimal low-rank regularized inverse matrix for various error measures. Numerical experiments demonstrate the benefits and potential applications of our approach to problems in signal and image processing.Comment: 24 pages, 11 figure

Concept of spinsonde for multi-cycle measurement of vertical wind profile of tropical cyclones

Tropical cyclones and cyclogenesis are active areas of research. Chute-operated dropsondes jointly developed by NASA and NCAR are capable of acquiring high resolution vertical wind profile of tropical cyclones. This paper proposes a chute-free vertical retardation technique (termed as spinsonde) that can accurately measure vertical wind profile. Unlike the expendable dropsondes, the spinsonde allows multi-cycle measurement to be performed within a single flight. Proof of principle is demonstrated using a simulation software and results indicate that the GPS ground speed correlates with the wind speeds to within +/-5 km/h. This technique reduces flying weight and increases payload capacity by eliminating bulky chutes. Maximum cruising speed (Vh) achieved by the spinsonde UAV is 372 km/h.Comment: arXiv admin note: substantial text overlap with arXiv:1407.845