Most existing video denoising algorithms assume a single statistical model of image noise, e.g. additive Gaussian white noise, which often is violated in practice. In this paper, we present a new patch-based video denoising algorithm capable of removing serious mixed noise from the video data. By grouping similar patches in both spatial and temporal domain, we formulate the problem of removing mixed noise as a low-rank matrix completion problem, which leads to a denoising scheme without strong assumptions on the statistical properties of noise. The resulting nuclear norm related minimization problem can be efficiently solved by many recent developed methods. The robustness and effectiveness of our proposed denoising algorithm on removing mixed noise, e.g. heavy Gaussian noise mixed with impulsive noise, is validated in the experiments and our proposed approach compares favorably against a few state-of-art denoising algorithms.

Abstract. This paper presents a new video restoration scheme based on the joint sparse and lowrank matrix approximation. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem. The resulted nuclear norm and 1 norm related minimization problem can also be efficiently solved by many recently developed numerical methods. The efficiency of the proposed video restoration scheme is illustrated on two applications: video denoising in the presence of random-valued noise and video in-painting for archived films. The numerical experiments indicated the proposed video restoration method is compared favorably against many existing algorithms.Key words. nuclear norm, low-rank matrix, sparse matrix, denoising, in-painting AMS subject classifications. 68U10, 65J22, 90C25, 65K051. Introduction. Even with today's advances in camera and digital sensor technology, video data collected in practice often suffers from many types of annoying degradations, e.g., noise contamination, image blurring and missing data. For example, video data can be quite noisy when captured at high sensitivities, such as low lighting condition, high ISO setting or high capture rate. The frames of video data can be blurred when there are fast moving objects in the scene or when there are camera shakes. Some parts of video data can be missing or invisible from a user perspective due to occlusions, scratches, or errors in data conversion/communication. The goal of video restoration is then to recover the original one from the obtained degraded video data. With the prevalence of webcams and camera phones, the problem of video restoration has become even more important than before.In recent years, patch-based image restoration scheme has emerged as one promising approach for various image restoration tasks, e.g. denoising and in-painting ([1, 2, 3]). The basic idea of these approaches is to regularize the restoration process by utilizing the spatial redundancy of original static images. Compared to static image data, video data tends to be of lower quality due to the high speed capturing rate of video camera, e.g. lower signal-to-noise ratio and lower image resolution. Meanwhile, owing to its significant temporal redundancy, video data usually provides much richer information about the scene than static image data does. Thus, the efficiency of restoring degraded video data largely depends on how efficient the temporal redundancy is utilized in the methods. Some of patched based image restoration methods have been extended to the case of video denoising ([4, 5]). Although differing from details, these video restoration methods are built upon the same methodology that exploits the self-similarity in video by examining the the similarity among different image patches.The aforementioned patch-based image/video restoration methods showed impressive results on suppressing image noise when the noise is mostly Gaussian white noise. In practice, the existence of ou...

A modified electro-mechanical impedance model of piezoelectric actuator-sensors is presented in this study. The presented model treats the bonding layer between a piezoelectric patch and a host structure as a spring-mass-damper system in the coupled electro-mechanical analysis. The effect of bonding layers on the dynamic interaction between piezoelectric actuator-sensors and host structures is thus taken into account. The model is then used for debonding detection of composite patches. A debonding model is accordingly developed. The debonding model uses infinitesimal-length springs to model the joint between a composite patch and its base structure. The spring stiffness varies with the joint rigidity and directly influences the structural mechanical impedance as well as the piezoelectric electric admittance. A numerical example is provided to reveal the effect of bonding layers and demonstrate the feasibility of the proposed detection method.

No abstract

We propose a dynamic portfolio choice model with the mean-variance criterion for log returns. The model yields time-consistent portfolio policies and is analytically tractable even under some incomplete market settings. The portfolio policies conform with conventional investment wisdom (e.g., richer people should invest more absolute amounts of money in risky assets; the longer the investment time horizon, the more proportional amount of money should be invested in risky assets; and for long-term investment, people should not short-sell major stock indices whose returns are higher than the risk-free rate), and the model provides a direct link with the constant relative risk aversion utility maximization in a complete market. This paper was accepted by Kay Giesecke, finance.