Total Variation Denoising with Slack Variables [Poster]
Abstract not provided.
97 MATHEMATICS AND COMPUTING↗
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Total Variation Diminishing (TVD) schemes of uniform accuracy
Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.
Hartwich, PETER-M.↗
Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation
Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.
Yee, H. C.↗
Long-Term Variations in Total Solar Irradiance
For more than a decade total solar irradiance has been monitored simultaneously from space by different satellites. The detection of total solar irradiance variations by satellite -based experiments during the past decade and a half has stimulated modeling efforts to help identify their causes and to provide estimates of irradiance data, using "proxy" indicators of solar activity, for the time intervals when no satellite observations exist. In this paper the variations in total solar irradiance observed by the Nimbus-7/ERB, SMM/ACRIM I, and UARS/ACRIM II radiometers are compared to the changes in sunspot darkening and the enhanced emission of bright magnetic elements, including faculae and the magnetic network. Quantitative indices of sunspot darkening have been derived from the area and position of sunspots published in the NOAA-WDC Solar Geophysical Data catalog. The Mg core-to-wing ratio, derived from the irradiance observations of Nimbus-7 and NOAA9 satellites, is used as a proxy for the bright magnetic elements. It has been found that a model, calculated from the Mg II core-to-wing ratio underestimates the observed total irradiance at the time of maximum and during the beginning of the declining portion of solar cycle 22 similar in behaviour just before the maximum of solar cycle 21. Similar results are found using He-line equivalent width and 10.7 cm radio flux which indicates that the current irradiance models are in general not capable to reproducing the changes observed in total solar irradiance.
total↗
Optimization of Total Variation-Regularized Problems using Inexact Proximal Solves
Inexact proximal framework for total-variation minimization.
Kouri, Drew Philip [Sandia National Laboratories (↗
Long-term variations in total solar and UV irradiances
The variations of total solar and UV irradiances during solar cycles 21 and 22 are compared. The total solar irradiance data used were obtained by the SMM/active cavity radiometer irradiance monitoring (ACRIM) 1, upper atmosphere research satellite (UARS)/ACRIM 2 and ERBS experiments. The space-based irradiance observations are compared to the Mount Wilson Magnetic Plage and Photometric Sunspot Index, which is derived from the area and position of sunspots published by the NOAA World Data Center Solar Geophysical Data Catalog. It is found that the variations in solar UV irradiance were similar during the maximum and minimum of solar cycles 21 and 22. The possible reasons for the differences in the irradiance values during the minima of the two solar cylces are discussed.
Pap, J. M.↗
Long-term variations in total solar irradiance
For more than a decade total solar irradiance has been monitored simultaneously from space by different satellites. The detection of total solar irradiance variations by satellite-based experiments during the past decade and a half has stimulated modeling efforts to help identify their causes and to provide estimates of irradiance data, using `proxy' indicators of solar activity, for time intervals when no satellite observations exist. In this paper total solar irradiance observed by the Nimbus-7/Earth Radiation Budget (ERB), Solar Maximum Mission (SMM)/Active Cavity Radiometer Irradiance Monitor (ACRIM) 1, and Upper Atmosphere Research Satellite (UARS)/ACRIM 2 radiometers is modeled with the Photometric Sunspot Index and the Mg II core-to-wing ratio. Since the formation of the Mg II line is very similar to that of the Ca II K line, the Mg core-to-wing ratio, derived from the irradiance observations of the Nimbus-7 and NOAA9 satellites, is used as a proxy for the bright magnetic elements. It is shown that the observed changes in solar irradiance are underestimated by the proxy models at the time of maximum and during the beginning of the declining portion of solar cycle 22 similar to behavior just before the maximum of solar cycle 21. This disagreement between total irradiance observations and their model estimates is indicative of the fact that the underlying physical mechanism of the changes observed in the solar radiative output is not well-understood. Furthermore, the uncertainties in the proxy data used for irradiance modeling and the resulting limitation of the models should be taken into account, especially when the irradiance models are used for climatic studies.
Pap, Judit M.↗
Utilization of 100 mb midlatitude height fields as an indicator of sampling effects on total ozone variations
Midlatitude 100-mb height fields are employed to determine the effects of ground based sampling locations on measurements of variations in the total ozone content of the atmosphere. The precision of the zonal average heights computed by the technique of Angell and Korshover (1978) from data over ozone sampling areas at 50 deg N is compared to the zonal average computed from the entire data set. Linear regressions of ozone contents determined by an analysis of backscatter UV satellite data with respect to 100 mb heights are utilized to transform zonal differences in height to ozone levels. The zonal average total ozone sampling error is found to be on the order of 2% for midlatitudes of the Northern hemisphere, indicating that the general shape of ozone trends determined by ground-based observations appears to be real and the increase of ozone from the mid-1960's to the early 1970's may be greater than previously suggested.
Miller, A. J.↗
Fast Multigrid Techniques in Total Variation-Based Image Reconstruction
Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.
Oman, Mary Ellen↗
Observational evidence and dynamical interpretation of the total ozone variations in the equatorial region
The total ozone amount is sensitive to the general circulation changes in the lower stratosphere due to the photochemically inactive nature of ozone there. In the equatorial region, such circulation changes arise from the quasi-biennial oscillation (QBO) of the stratospheric zonal wind and the El Nino/Southern Oscillation (ENSO). In the first half of this study we present observational results of the long-term variations in the equatorial ozone field using the 11 year Total Ozone Mapping Spectrometer (TOMS) data, by paying special attention to the longitudinal structure. In the latter half we try to understand quantitatively these variations by using a simple mechanistic relationship. We hypothesis that the ozone modulating processes are attributable to two dynamical effects, the advection effect and tropopause effect, owing to the strong vertical stratification of ozone existing just above the tropopause. The advection effect comes from the vertical motion which maintains the temperature structure, compensating for the radiative damping. The tropopause effect is associated with the altitude change of the tropopause. The total ozone variations in the tropics is discussed in terms of these two dynamical processes with the aid of mechanistic equations combined with the wind and sea surface temperature (SST) observations. The interactions between tropical and extratropical latitudes are beyond the scope of this study. Photochemical effects are also neglected. Details of this study are given by Shiotani (1992) and Hasebe (1992).
Shiotani, Masato↗
Efficient implementation of essentially non-oscillatory shock capturing schemes
In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total-variation-diminishing), TVB (total-variation-bounded) and the recently developed ENO (essentially non-oscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple TVD Runge-Kutta type time discretization, and an ENO construction procedure based on fluxes rather than on cell averages. These improvements simplify the schemes considerably -- especially for multi-dimensional problems or problems with forcing terms. Preliminary numerical results are also given.
Shu, Chi-Wang↗
Efficient implementation of essentially non-oscillatory shock-capturing schemes
In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total-variation-diminishing), TVB (total-variation-bounded) and the recently developed ENO (essentially non-oscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple TVD Runge-Kutta type time discretization, and an ENO construction procedure based on fluxes rather than on cell averages. These improvements simplify the schemes considerably - especially for multi-dimensional problems or problems with forcing terms. Preliminary numerical results are also given.
Shu, Chi-Wang↗
A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids
A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.
Wang, Z. J.↗
High-Order Spectral Volume Method for 2D Euler Equations
The Spectral Volume (SV) method is extended to the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. Solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.
Wang, Z. J.↗
The global distribution of long-term total ozone variations during the period 1957-1975
Total ozone observations in the international network have been used as a basis for the analysis of the mean monthly ozone distribution over the globe for the period 1957-1975. It has been found that during the period 1961-1970 the total ozone amount increased in the Northern Hemisphere by about 12 percent and that this increase seems to be significant at all latitudes. Although the data were sparse for the Southern Hemisphere, there did not appear to be any significant ozone changes during the 10 year period. Relatively large geographic variations were found in the ozone trends and it is suggested that these variations are related to large scale changes in the atmospheric circular pattern.
London, J.↗
Seasonal Variation of Total Mercury Burden in the American Alligator (Alligator Mississippiensis) at Merritt Island National Wildlife Refuge (MINWR), Florida
Seasonal variation of mercury (Hg) is not well studied in free-ranging wildlife. Atmospheric deposition patterns of Hg have been studied in detail and have been modeled for both global and specific locations with great accuracy and correlates to environment impact. However, monitoring these trends in wildlife is complicated due to local environmental parameters (e.g., rainfall, humidity, pH, bacterial composition) that can affect the transformation of atmospheric Hg to the biologically available forms. Here, we utilized an abundant and healthy population of American alligators (Alligator mississippiensis) at Merritt Island National Wildlife Refuge (MINWR), FL, and assessed Hg burden in whole blood samples over a span of 7 years (2007 2014; n 174) in an effort to assess seasonal variation of total [Hg]. While the majority of this population is assumed healthy, 18 individuals with low body mass indices (BMI, defined in this study) were captured throughout the 7 year sampling period. These individual alligators exhibited [Hg] that were not consistent with the observed overall seasonal [Hg] variation, and were statistically different from the healthy population of alligators. The alligators with low BMI had elevated concentrations of Hg compared to their age/sex/season matched counterparts with normal BMI. Statistically significant differences were found between the winter and spring seasons for animals with normal BMI. The data in this report supports the conclusion that organismal total [Hg] do fluctuate directly with seasonal deposition rates as well as other seasonal environmental parameters, such as average rainfall and prevailing wind direction. This study highlights the unique environment of MINWR to permit annual assessment of apex predators, such as the American alligator, to determine detailed environmental impact of contaminants of concern.
Hg↗
Ultrasound waveform tomography with spatial and edge regularization
Synthetic-aperture ultrasound tomography systems and methods using scanning arrays and algorithms configured to simultaneously acquire ultrasound transmission and reflection data, and process the data for improved ultrasound tomography imaging, wherein the tomography imaging comprises total-variation regularization, or a modified total variation regularization, particularly with edge-guided or spatially variant regularization.
Huang, Lianjie↗
Seasonal and interannual variations in total ozone revealed by the Nimbus-4 backscattered ultraviolet experiment
The first two years of Backscattered Ultraviolet (BUV) ozone data from the Nimbus-4 spacecraft were reprocessed. The seasonal variations of total ozone for the period April 1970 to April 1972 are described using daily zonal means to 10 deg latitude zones and a time-latitude cross section. In addition, the BUV data are compared with analyzed Dobson data and with IRIS data also obtained from the Nimbus-4 spacecraft. A harmonic analysis was performed on the daily zonal means. Amplitudes, days of peaks, and percentage of variance were computed for annual and semi-annual waves and for higher harmonics of an annual period for the two years. Asymmetries are found in the annual waves in the two hemispheres, with a subtle interannual difference which may be due to changes in the general circulation. A significant semi-annual component is detected in the tropics for the first year, which appears to result from influences of the annual waves in the two hemispheres.
Hilsenrath, E.↗