This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions that preserve the phase of the complex-valued wavelet coefficients and those that do not. The new procedure exhibits excellent quantitative and visual performance, which is demonstrated by simulation on standard test images.
In this article, we propose a denoising methodology in the wavelet domain based on a Bayesian hierarchical model using Double Weibull prior. We propose two estimators, one based on posterior mean (Double Weibull Wavelet Shrinker, DWWS) and the other based on larger posterior mode (DWWS-LPM), and show how to calculate them efficiently. Traditionally, mixture priors have been used for modeling sparse wavelet coefficients. The interesting feature of this article is the use of non-mixture prior. We show that the methodology provides good denoising performance, comparable even to state-of-the-art methods that use mixture priors and empirical Bayes setting of hyperparameters, which is demonstrated by extensive simulations on standardly used test functions. An application to real-word dataset is also considered.
This research is the first use of Box-Jenkins time-series models to describe changes in heart rate (HR) of free-ranging crossbred cows (Bos taurus) receiving both programmed audio cues from directional virtual fencing (DVF TM) devices and non-programmed environmental/physiological cues. The DVF TM device is designed to control the animal's location on the landscape. Polar Accurex® devices were used to capture HR every minute between 19 and 24 March 2003, when three mature free-ranging beef cows, previously habituated to the DVF TM device, were confined to a brush-infested area of an arid rangeland paddock. Global positioning system (GPS) electronics were used to record each cow's location approximately every minute while it was in a 58 ha virtual paddock (VP TM) and every second when it penetrated a virtual boundary (VB TM). The cows never escaped through the VB TM , although they penetrated it a total of 26 times in 11 different events, at which times they received programmed audio cues lasting from 1 to 56 s. Plots of these data reveal that HR spikes from programmed audio cues all fell within textbook range for cow HR (40-186 beats per minute, bpm). Heart rate spikes were analyzed using Box-Jenkins intervention analysis models, which showed that for both audio and selected environmental/physiological events, HR spikes typically returned to pre-cuing "baseline" levels in about one minute. However, the longest return-time to baseline (about four minutes) was for an environmental/physiological event of unknown origin. HR, animal location, weather and other electronic data should be measured at equally-spaced time intervals using a single time stamp to accurately associate HR changes with possible causes.
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