Recent progress in random metric theory and its applications to conditional risk measures

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measures. Section 2 gives the central framework in random metric theory, topological structures, important examples, the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals. Section 3 gives several important representation theorems for random conjugate spaces. Section 4 gives characterizations for a complete random normed module to be random reflexive. Section 5 gives hyperplane separation theorems currently available in random locally convex modules. Section 6 gives the theory of random duality with respect to the locally $L^{0}-$convex topology and in particular a characterization for a locally $L^{0}-$convex module to be $L^{0}-$pre$-$barreled. Section 7 gives some basic results on $L^{0}-$convex analysis together with some applications to conditional risk measures. Finally, Section 8 is devoted to extensions of conditional convex risk measures, which shows that every representable $L^{\infty}-$type of conditional convex risk measure and every continuous $L^{p}-$type of convex conditional risk measure ($1\leq p<+\infty$) can be extended to an $L^{\infty}_{\cal F}({\cal E})-$type of $\sigma_{\epsilon,\lambda}(L^{\infty}_{\cal F}({\cal E}), L^{1}_{\cal F}({\cal E}))-$lower semicontinuous conditional convex risk measure and an $L^{p}_{\cal F}({\cal E})-$type of ${\cal T}_{\epsilon,\lambda}-$continuous conditional convex risk measure ($1\leq p<+\infty$), respectively.Comment: 37 page

A systematic algorithm development for image processing feature extraction in automatic visual inspection : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology in the Department of Production Technology, Massey University

Image processing techniques applied to modern quality control are described together with the development of feature extraction algorithms for automatic visual inspection. A real-time image processing hardware system already available in the Department of Production Technology is described and has been tested systematically for establishing an optimal threshold function. This systematic testing has been concerned with edge strength and system noise information. With the a priori information of system signal and noise, non-linear threshold functions have been established for real time edge detection. The performance of adaptive thresholding is described and the usefulness of this nonlinear approach is demonstrated from results using machined test samples. Examination and comparisons of thresholding techniques applied to several edge detection operators are presented. It is concluded that, the Roberts' operator with a non-linear thresholding function has the advantages of being simple, fast, accurate and cost effective in automatic visual inspection

A Fast DOA Estimation Algorithm Based on Polarization MUSIC

A fast DOA estimation algorithm developed from MUSIC, which also benefits from the processing of the signals' polarization information, is presented. Besides performance enhancement in precision and resolution, the proposed algorithm can be exerted on various forms of polarization sensitive arrays, without specific requirement on the array's pattern. Depending on the continuity property of the space spectrum, a huge amount of computation incurred in the calculation of 4-D space spectrum is averted. Performance and computation complexity analysis of the proposed algorithm is discussed and the simulation results are presented. Compared with conventional MUSIC, it is indicated that the proposed algorithm has considerable advantage in aspects of precision and resolution, with a low computation complexity proportional to a conventional 2-D MUSIC