A Bayesian Hyperprior Approach for Joint Image Denoising and Interpolation, with an Application to HDR Imaging

Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an approach is particularly unstable for most inverse problems beyond denoising. In this work, we propose the use of a hyperprior to model image patches, in order to stabilize the estimation procedure. There are two main advantages to the proposed restoration scheme: Firstly it is adapted to diagonal degradation matrices, and in particular to missing data problems (e.g. inpainting of missing pixels or zooming). Secondly it can deal with signal dependent noise models, particularly suited to digital cameras. As such, the scheme is especially adapted to computational photography. In order to illustrate this point, we provide an application to high dynamic range imaging from a single image taken with a modified sensor, which shows the effectiveness of the proposed scheme.Comment: Some figures are reduced to comply with arxiv's size constraints. Full size images are available as HAL technical report hal-01107519v5, IEEE Transactions on Computational Imaging, 201

A practical degradation based method to predict long-term moisture incursion and colour change in high power LEDs

The effect of relative humidity on LEDs and how the moisture incursion is associated to the color shift is studied. This paper proposes a different approach to describe the lumen degradation of LEDs due to the long-term effects of humidity. Using the lumen degradation data of different types of LEDs under varying conditions of relative humidity, a humidity based degradation model (HBDM) is developed. A practical estimation method from the degradation behaviour is proposed to quantitatively gauge the effect of moisture incursion by means of a humidity index. This index demonstrates a high correlation with the color shift indicated by the LED's yellow to blue output intensity ratio. Physical analyses of the LEDs provide a qualitative validation of the model, which provides good accuracy with longer periods of moisture exposure. The results demonstrate that the HBDM is an effective indicator to predict the extent of the long-term impact of humidity and associated relative color shift

Gaussian Process Regression for In-situ Capacity Estimation of Lithium-ion Batteries

Accurate on-board capacity estimation is of critical importance in lithium-ion battery applications. Battery charging/discharging often occurs under a constant current load, and hence voltage vs. time measurements under this condition may be accessible in practice. This paper presents a data-driven diagnostic technique, Gaussian Process regression for In-situ Capacity Estimation (GP-ICE), which estimates battery capacity using voltage measurements over short periods of galvanostatic operation. Unlike previous works, GP-ICE does not rely on interpreting the voltage-time data as Incremental Capacity (IC) or Differential Voltage (DV) curves. This overcomes the need to differentiate the voltage-time data (a process which amplifies measurement noise), and the requirement that the range of voltage measurements encompasses the peaks in the IC/DV curves. GP-ICE is applied to two datasets, consisting of 8 and 20 cells respectively. In each case, within certain voltage ranges, as little as 10 seconds of galvanostatic operation enables capacity estimates with approximately 2-3% RMSE.Comment: 12 pages, 10 figures, submitted to IEEE Transactions on Industrial Informatic

Statistical modelling of railway track geometry degradation using hierarchical Bayesian models

Railway maintenance planners require a predictive model that can assess the railway track geometry degradation. The present paper uses a hierarchical Bayesian model as a tool to model the main two quality indicators related to railway track geometry degradation: the standard deviation of longitudinal level defects and the standard deviation of horizontal alignment defects. Hierarchical Bayesian Models (HBM) are flexible statistical models that allow specifying different spatially correlated components between consecutive track sections, namely for the deterioration rates and the initial qualities parameters. HBM are developed for both quality indicators, conducting an extensive comparison between candidate models and a sensitivity analysis on prior distributions. HBM is applied to provide an overall assessment of the degradation of railway track geometry, for the main Portuguese railway line Lisbon-Oporto

Development of Probabilistic Corrosion Growth Models with Applications in Integrity Management of Pipelines

Metal-loss corrosion is a major threat to the structural integrity and safe operation of underground oil and gas pipelines worldwide. The reliability-based corrosion management program has been increasingly used in the pipeline industry, which typically includes three tasks, namely periodic high-resolution inline inspections (ILIs) to detect and size corrosion defects on a given pipeline, engineering critical assessment of the corrosion defects reported by the inspection tool and mitigation of defects. This study addresses the core involved in the reliability-based corrosion management program. First, the stochastic process in conjunction with the hierarchical Bayesian methodology is used to characterize the growth of defect depth using imperfect ILI data. The biases, random scattering errors as well as the correlations between the random scattering errors associated with the ILI tools are accounted for in the Bayesian inference. The Markov Chain Monte Carlo (MCMC) simulation techniques are employed to carry out the Bayesian updating and numerically evaluate the posterior distributions of the parameters in the growth model. Second, a simulation-based methodology is presented to evaluate the time-dependent system reliability of pressurized energy pipelines containing multiple active metal-loss corrosion defects using the developed growth models. Lastly, a probabilistic investigation is carried out to determine the optimal inspection interval for the newly-built onshore underground natural gas pipelines with respect to external metal-loss corrosion by considering the generation of corrosion defects over time and time-dependent growth of individual defects. The proposed methodology will facilitate the reliability-based corrosion management for corroding pipelines

Models for Data Analysis in Accelerated Reliability Growth

This work develops new methodologies for analyzing accelerated testing data in the context of a reliability growth program for a complex multi-component system. Each component has multiple failure modes and the growth program consists of multiple test-fix stages with corrective actions applied at the end of each stage. The first group of methods considers time-to-failure data and test covariates for predicting the final reliability of the system. The time-to-failure of each failure mode is assumed to follow a Weibull distribution with rate parameter proportional to an acceleration factor. Acceleration factors are specific to each failure mode and test covariates. We develop a Bayesian methodology to analyze the data by assigning a prior distribution to each model parameter, developing a sequential Metropolis-Hastings procedure to sample the posterior distribution of the model parameters, and deriving closed form expressions to aggregate component reliability information to assess the reliability of the system. The second group of methods considers degradation data for predicting the final reliability of a system. First, we provide a non-parametric methodology for a single degradation process. The methodology utilizes functional data analysis to predict the mean time-to-degradation function and Gaussian processes to capture unit-specific deviations from the mean function. Second, we develop parametric model for a component with multiple dependent monotone degradation processes. The model considers random effects on the degradation parameters and a parametric life-stress relationship. The assumptions are that degradation increments follow an Inverse Gaussian process and a Copula function captures the dependency between them. We develop a Bayesian and a maximum likelihood procedure for estimating the model parameters using a two-stage process: (1) estimate the parameters of the degradation processes as if they were independent and (2) estimate the parameters of the Copula function using the estimated cumulative distribution function of the observed degradation increments as observed data. Simulation studies show the efficacy of the proposed methodologies for analyzing multi-stage reliability growth data