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It is known that many image enhancement methods have a tradeoff between noise suppression and edge enhancement. In this paper, we propose a new technique for image enhancement filtering and explain it in human visual perception theory. It combines kernel regression and local homogeneity and evaluates the restoration performance of smoothing method. First, image is filtered in kernel regression. Then image local homogeneity computation is introduced which offers adaptive selection about further smoothing. The overall effect of this algorithm is effective about noise reduction and edge enhancement. Experiment results show that this algorithm has better performance in image edge enhancement, contrast enhancement, and noise suppression.

This paper considered a dependent discrete-time risk model, in which the insurance risks are represented by a sequence of independent and identically distributed real-valued random variables with a common Gamma-like tailed distribution; the financial risks are denoted by another sequence of independent and identically distributed positive random variables with a finite upper endpoint, but a general dependence structure exists between each pair of the insurance risks and the financial risks. Following the works of Yang and Yuen in 2016, we derive some asymptotic relations for the finite-time and infinite-time ruin probabilities. As a complement, we demonstrate our obtained result through a Crude Monte Carlo (CMC) simulation with asymptotics.

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In many applications, observed signals are contaminated by both random noise and blur. This paper proposes a blind deconvolution procedure for estimating a regression function with possible jumps preserved, by removing both noise and blur when recovering the signals. Our procedure is based on three local linear kernel estimates of the regression function, constructed from observations in a left-side, a right-side, and a two-side neighborhood of a given point, respectively. The estimated function at the given point is then defined by one of the three estimates with the smallest weighted residual sum of squares. To better remove the noise and blur, this estimate can also be updated iteratively. Performance of this procedure is investigated by both simulation and real data examples, from which it can be seen that our procedure performs well in various cases.

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