Inhomogeneous Noise Research Articles

Maximum a posteriori CMB lensing reconstruction

Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, $\rm{LensIt}$, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The method achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor $\simeq 2 $ compared to the quadratic estimator in a CMB stage IV configuration.

Efficient and robust cell detection: A structured regression approach.

Efficient and robust cell detection serves as a critical prerequisite for many subsequent biomedical image analysis methods and computer-aided diagnosis (CAD). It remains a challenging task due to touching cells, inhomogeneous background noise, and large variations in cell sizes and shapes. In addition, the ever-increasing amount of available datasets and the high resolution of whole-slice scanned images pose a further demand for efficient processing algorithms. In this paper, we present a novel structured regression model based on a proposed fully residual convolutional neural network for efficient cell detection. For each testing image, our model learns to produce a dense proximity map that exhibits higher responses at locations near cell centers. Our method only requires a few training images with weak annotations (just one dot indicating the cell centroids). We have extensively evaluated our method using four different datasets, covering different microscopy staining methods (e.g., H & E or Ki-67 staining) or image acquisition techniques (e.g., bright-filed image or phase contrast). Experimental results demonstrate the superiority of our method over existing state of the art methods in terms of both detection accuracy and running time.

Ambient noise tomography across Mount St. Helens using a dense seismic array

AbstractWe investigated upper crustal structure with data from a dense seismic array deployed around Mount St. Helens for 2 weeks in the summer of 2014. Interstation cross correlations of ambient seismic noise data from the array were obtained, and clear fundamental mode Rayleigh waves were observed between 2.5 and 5 s periods. In addition, higher‐mode signals were observed around 2 s period. Frequency‐time analysis was applied to measure fundamental mode Rayleigh wave phase velocities, which were used to invert for 2‐D phase velocity maps. An azimuth‐dependent traveltime correction was implemented to mitigate potential biases introduced due to an inhomogeneous noise source distribution. Reliable phase velocity maps were only obtained between 3 and 4 s periods due to limitations imposed by the array aperture and higher‐mode contamination. The phase velocity tomography results, which are sensitive to structure shallower than 6 km depth, reveal an ~10–15% low‐velocity anomaly centered beneath the volcanic edifice and peripheral high‐velocity anomalies that likely correspond to cooled igneous intrusions. We suggest that the low‐velocity anomaly reflects the high‐porosity mixture of lava and ash deposits near the surface of the edifice, a highly fractured magmatic conduit and hydrothermal system beneath the volcano, and possibly a small contribution from silicate melt.

Wiener filter reloaded: fast signal reconstruction without preconditioning

We present a high performance solution to the Wiener filtering problem via a formulation that is dual to the recently developed messenger technique. This new dual messenger algorithm, like its predecessor, efficiently calculates the Wiener filter solution of large and complex data sets without preconditioning and can account for inhomogeneous noise distributions and arbitrary mask geometries. We demonstrate the capabilities of this scheme in signal reconstruction by applying it on a simulated cosmic microwave background (CMB) temperature data set. The performance of this new method is compared to that of the standard messenger algorithm and the preconditioned conjugate gradient (PCG) approach, using a series of well-known convergence diagnostics and their processing times, for the particular problem under consideration. This variant of the messenger algorithm matches the performance of the PCG method in terms of the effectiveness of reconstruction of the input angular power spectrum and converges smoothly to the final solution. The dual messenger algorithm outperforms the standard messenger and PCG methods in terms of execution time, as it runs to completion around 2 and 3-4 times faster than the respective methods, for the specific problem considered.

A pseudo-spectrum analysis of galaxy–galaxy lensing

We present the application of the pseudo-spectrum method to galaxy-galaxy lensing. We derive explicit expressions for the pseudo-spectrum analysis of the galaxy-shear cross spectrum, which is the Fourier space counterpart of the stacked galaxy-galaxy lensing profile. The pseudo-spectrum method corrects observational issues such as the survey geometry, masks of bright stars and their spikes, and inhomogeneous noise, which distort the spectrum and also mix the E-mode and the B-mode signals. Using ray-tracing simulations in N-body simulations including realistic masks, we confirm that the pseudo-spectrum method successfully recovers the input galaxy-shear cross spectrum. We also investigate the covariance of the galaxy-shear cross spectrum using the ray-tracing simulations to show that there is an excess covariance relative to the Gaussian covariance at small scales where the shot noise is dominated in the Gaussian approximation. We find that the excess of the covariance is consistent with the expectation from the halo sample variance (HSV), which originates from the matter fluctuations at scales larger than the survey area. We apply the pseudo-spectrum method to the observational data of Canada-France-Hawaii Telescope Lensing survey (CFHTLenS) shear catalogue and three different spectroscopic samples of Sloan Digital Sky Survey Luminous Red Galaxy (SDSS LRG), and Baryon Oscillation Spectroscopic Survey (BOSS) CMASS and LOWZ galaxies. The galaxy-shear cross spectra are significantly detected at the level of 7-10$\sigma$ using the analytic covariance with the HSV contribution included. We also confirm that the observed spectra are consistent with the halo model predictions with the halo occupation distribution parameters estimated from previous work. This work demonstrates the viability of galaxy-galaxy lensing analysis in the Fourier space.

Local analyses ofPlanckmaps with Minkowski functionals

Minkowski Functionals (MF) are excellent tools to investigate the statistical properties of the cosmic background radiation (CMB) maps. Between their notorious advantages is the possibility to use them efficiently in patches of the CMB sphere, which allow studies in masked skies, inclusive analyses of small sky regions. Then, possible deviations from Gaussianity are investigated by comparison with MF obtained from a set of Gaussian isotropic simulated CMB maps to which are applied the same cut-sky masks. These analyses are sensitive enough to detect contaminations of small intensity like primary and secondary CMB anisotropies. Our methodology uses the MF, widely employed to study non-Gaussianities in CMB data, and asserts Gaussian deviations only when all of them points out an exceptional $\chi^2$ value, at more than $2.2 \sigma$ confidence level, in a given sky patch. Following this rigorous procedure, we find 13 regions in the foreground-cleaned Planck maps that evince such high levels of non-Gaussian deviations. According to our results, these non-Gaussian contributions show signatures that can be associated to the presence of hot or cold spots in such regions. Moreover, some of these non-Gaussian deviations signals suggest the presence of foreground residuals in those regions located near the galactic plane. Additionally, we confirm that most of the regions revealed in our analyses, but not all, have been recently reported in studies done by the Planck collaboration. Furthermore, we also investigate whether these non-Gaussian deviations can be possibly sourced by systematics, like inhomogeneous noise and beam effect in the released Planck data, or perhaps due to residual galactic foregrounds.

Adaptive fuzzy c‐means algorithm based on local noise detecting for image segmentation

Adding spatial penalty terms in fuzzy c-means (FCM) models is an important approach for reducing the noise effects in the process of image segmentation. Though these algorithms have improved the robustness to noises in a certain extent, they still have some shortcomings. First, they are usually very sensitive to the parameters which are supposed to be tuned according to noise intensities. Second, in the case of inhomogeneous noises, using a constant parameter for different image regions is obviously unreasonable and usually leads to an unideal segmentation result. For overcoming these drawbacks, a noise detecting-based adaptive FCM for image segmentation is proposed in this study. Two image filtering methods, playing the roles of denoising and maintaining detail information are utilised in the new algorithm. The parameters for balancing these two parts are computed by measuring the variance of grey-level values in each neighbourhood. Numerical experiments on both synthetic and real-world image data show that the new algorithm is effective and efficient.

Noise-mediated Casimir-like pulse interaction mechanism in lasers

Strongly pumped mode-locked lasers often form pulse bunches. Although several mechanisms of pulse interaction are known, none yields the experimentally observed long-range attraction. Here we demonstrate theoretically and experimentally a new pulse interaction mechanism mediated by the continuum noise floor that is a universal feature in multipulse passively mode-locked lasers. Long-range attraction is facilitated by the depletion of the gain by the pulses, leading to an inhomogeneous noise floor that biases the timing jitter of the pulses and produces an effective interpulse potential with stable pulse bunch configurations. The pulses attract by suppressing electromagnetic fluctuations, as do conductors in the Casimir effect of quantum electrodynamics. This enables manipulation and design of multipulse waveforms to ultimately make them useful for application of mode-locked lasers.

Physical origin of nonequilibrium fluctuation-induced forces in fluids.

Long-range thermal fluctuations appear in fluids in nonequilibrium states leading to fluctuation-induced Casimir-like forces. Two distinct mechanisms have been identified for the origin of the long-range nonequilibrium fluctuations in fluids subjected to a temperature or concentration gradient. One is a coupling between the heat or mass-diffusion mode with a viscous mode in fluids subjected to a temperature or concentration gradient. Another one is the spatial inhomogeneity of thermal noise in the presence of a gradient. We show that in fluids fluctuation-induced forces arising from mode coupling are several orders of magnitude larger than those from inhomogeneous noise.

Quadrilateral Scaled Threshold Weighted Averaging Filter for MRI Denoising

Image denoising of Magnetic Resonance Imaging (MRI) by manifold approach focuses on the removal of inhomogeneous Gaussian and Rician noise without blurring the fine anatomical structures. Non Local Means (NLM) filter, the popular denoising technique, does not hold well for edge preservation of images with low Signal to Noise Ratio (SNR). Hence, an alternative formulation of NLM filter is required. This paper presents a quadrilateral scaling method based on image gradients for change in the isotropic nature of NLM and provides an estimate for edge orientation. A new definition of NLM weights based on similarity intensity measures that reflect on the noise statistics is introduced. The efficacy and feasibility of the proposed method is demonstrated through simulation. The probable reduction in time consumption is illustrated.

North-South non-Gaussian asymmetry in Planck CMB maps

We report the results of a statistical analysis performed with the four foreground-cleaned Planck maps by means of a suitably defined local-variance estimator. Our analysis shows a clear dipolar structure in Planck's variance map pointing in the direction (l,b) ≃ (220°,-32°), thus consistent with the North-South asymmetry phenomenon. Surprisingly, and contrary to previous findings, removing the CMB quadrupole and octopole makes the asymmetry stronger. Our results show a maximal statistical significance, of 98.1% CL, in the scales ranging from ℓ=4 to ℓ=500. Additionally, through exhaustive analyses of the four foreground-cleaned and individual frequency Planck maps, we find unlikely that residual foregrounds could be causing this dipole variance asymmetry. Moreover, we find that the dipole gets lower amplitudes for larger masks, evidencing that most of the contribution to the variance dipole comes from a region near the galactic plane. Finally, our results are robust against different foreground cleaning procedures, different Planck masks, pixelization parameters, and the addition of inhomogeneous real noise.

Optimal estimator for the amplitude of the bispectrum from infrared clustered sources

We devise a fast and optimal estimator for the amplitude of the bispectrum of clustered Infrared (IR) point-sources. We show how this estimator can account for the cases of partial sky coverage and inhomogeneous noise. Expected detection significance are presented in terms of signal-to-noise, finding that the IR bispectrum will realistically be undetectable below 220 GHz with a Planck-like experiment; on the contrary detection may be achieved at, or above, 220 GHz especially if the CMB is removed. We also show how this estimator can be combined with estimators of radio and CMB non-Gaussianity to build up joint robust constraints. On the one hand, we find that, for a Planck-like experiment, CMB non-Gaussianity estimation can be decoupled from point-source contributions, unless few sources are masked. On the other hand, we find that the estimation of radio and IR non-Gaussianity are strongly coupled, which diminishes their separate detection significance.

Managing uncertainty in early estimation of epidemic behaviors using scenario trees

The onset of an epidemic can be foreshadowed theoretically through observation of a number of syndromic signals, such as absenteeism or rising sales of particular pharmaceuticals. The success of such approaches depends on how well the uncertainty associated with the early stages of an epidemic can be managed. This article uses scenario trees to summarize the uncertainty in the parameters defining an epidemiological process and the future path the epidemic might take. Extensive simulations are used to generate various syndromic and epidemic time series, which are then summarized in scenario trees, creating a simple data structure that can be explored quickly at surveillance time without the need to fit models. Decisions can be made based on the subset of the uncertainty (the subtree) that best fits the current observed syndromic signals. Simulations are performed to investigate how well an underlying dynamic model of an epidemic with inhomogeneous mixing and noise fluctuations can capture the effects of social interactions. Two noise terms are introduced to capture the observable fluctuations in the social network connectivity and variation in some model parameters (e.g., infectious time). Finally, it is shown how the entire framework can be used to compare syndromic surveillance systems against each other; to evaluate the effect of lag and noise on accuracy; and to evaluate the impact that differences in syndromic behavior among susceptible and infected populations have on accuracy.

Optical spin noise of a single hole spin localized in an (InGa)As quantum dot.

We advance spin noise spectroscopy to the ultimate limit of single spin detection. This technique enables the measurement of the spin dynamic of a single heavy hole localized in a flat (InGa)As quantum dot. Magnetic field and light intensity dependent studies reveal even at low magnetic fields a strong magnetic field dependence of the longitudinal heavy hole spin relaxation time with an extremely long T1 of ≥180 μs at 31mT and 5K. The wavelength dependence of the spin noise power discloses for finite light intensities an inhomogeneous single quantum dot spin noise spectrum which is explained by charge fluctuations in the direct neighborhood of the quantum dot. The charge fluctuations are corroborated by the distinct intensity dependence of the effective spin relaxation rate.

Optimal analysis of azimuthal features in the CMB

We present algorithms for searching for azimuthally symmetric features in CMB data. Our algorithms are fully optimal for masked all-sky data with inhomogeneous noise, computationally fast, simple to implement, and make no approximations. We show how to implement the optimal analysis in both Bayesian and frequentist cases. In the Bayesian case, our algorithm for evaluating the posterior likelihood is so fast that we can do a brute-force search over parameter space, rather than using a Monte Carlo Markov chain. Our motivating example is searching for bubble collisions, a pre-inflationary signal which can be generated if multiple tunneling events occur in an eternally inflating spacetime, but our algorithms are general and should be useful in other contexts.

New approaches to probing Minkowski functionals

We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of cosmic microwave background (CMB) maps in several domains: in real space (where they are commonly known as cumulant-correlators), and in harmonic and needlet bases. The essential aim is to retain more information than normally contained in these statistics, in order to assist in determining the source of any measured non-Gaussianity, in the same spirit as Munshi & Heavens skew-spectra were used to identify foreground contaminants to the CMB bispectrum in Planck data. Using a perturbative series to construct the Minkowski functionals (MFs), we provide a pseudo-|${\cal C}_\ell$| based approach in both harmonic and needlet representations to estimate these spectra in the presence of a mask and inhomogeneous noise. Assuming homogeneous noise, we present approximate expressions for error covariance for the purpose of joint estimation of these spectra. We present specific results for four different models of primordial non-Gaussianity local, equilateral, orthogonal and enfolded models, as well as non-Gaussianity caused by unsubtracted point sources. Closed form results of next-order corrections to MFs too are obtained in terms of a quadruplet of kurt-spectra. We also use the method of modal decomposition of the bispectrum and trispectrum to reconstruct the MFs as an alternative method of reconstruction of morphological properties of CMB maps. Finally, we introduce the odd-parity skew-spectra to probe the odd-parity bispectrum and its impact on the morphology of the CMB sky. Although developed for the CMB, the generic results obtained here can be useful in other areas of cosmology.

Random errors in carbon and water vapor fluxes assessed with Gaussian Processes

The flow of carbon between terrestrial ecosystems and the atmosphere is mainly driven by nonlinear, complex and time-lagged processes. Understanding the associated ecosystem responses is a key challenge regarding climate change questions such as the future development of the terrestrial carbon sink. However, high temporal resolution measurements of ecosystem variables (with the eddy covariance method) are subject to random error, that needs to be accounted for in model-data fusion, multi-site syntheses and up-scaling efforts.Gaussian Processes (GPs), a nonparametric regression method, have recently been shown to capture relationships in high-dimensional, nonlinear and noisy data. Heteroscedastic Gaussian Processes (HGPs) are a specialized GP method for data with inhomogeneous noise variance, such as eddy covariance measurements.Here, it is demonstrated that the HGP model captures measurement noise variances well, outperforming the model residual method and providing reasonable flux predictions at the same time. Based on meteorological drivers and temporal information, uncertainties of annual sums of carbon flux and water vapor flux at six different tower sites in Europe and North America are estimated. Similar noise patterns with different magnitudes were found across sites. Random uncertainties in annual sums of carbon fluxes were between 9.80 and 31.57gCm−2yr−1 (or 4–9% of the annual flux), and were between 2.54 and 8.13mmyr−1 (or 1–2% of the annual flux) for water vapor fluxes. The empirical HGP model offers a general method to estimate random errors at half-hourly resolution based on entire annual records of measurements. It is introduced as a new tool for random uncertainty assessment widely throughout the FLUXNET network.

Interaction of Additive Noise and Nonlinear Dynamics in the Double-Gyre Wind-Driven Ocean Circulation

Abstract In this paper the authors study the interactions of additive noise and nonlinear dynamics in a quasigeostrophic model of the double-gyre wind-driven ocean circulation. The recently developed framework of dynamically orthogonal field theory is used to determine the statistics of the flows that arise through successive bifurcations of the system as the ratio of forcing to friction is increased. This study focuses on the understanding of the role of the spatial and temporal coherence of the noise in the wind stress forcing. When the wind stress noise is temporally white, the statistics of the stochastic double-gyre flow does not depend on the spatial structure and amplitude of the noise. This implies that a spatially inhomogeneous noise forcing in the wind stress field only has an effect on the dynamics of the flow when the noise is temporally colored. The latter kind of stochastic forcing may cause more complex or more coherent dynamics depending on its spatial correlation properties.

Inhomogeneous Noise Correction Combined with Uniform Filter and Sensitivity Map (INCUS) for Multi-coil Imaging Including Parallel Imaging

We have developed and assess INCUS (inhomogeneous noise correction combined with uniform filter and sensitivity map), a novel technique to correct spatially inhomogeneous noise in surface-coil-based standard or parallel imaging in magnetic resonance (MR) imaging. We employed a weighted summation of 2 images uniformly filtered with both a strong filter and a weak or no filter to achieve spatially nonuniform filtering by utilizing a coil-sensitivity and/or noise map to give greater weight to the strongly denoised components of the region with lower signal-to-noise ratio (SNR). We compared the image quality and difference between INCUS and standard uniform filter techniques employing several types of linear or nonlinear filter in abdominal or diffusion-weighted brain images each for 1 volunteer acquired on a 1.5-tesla magnetic resonance (MR) imager with parallel imaging after adding simulated noise. The INCUS technique inherently reduced inhomogeneous noise on multiple surface-coil imaging and minimized blur obtained with every filter type. Overall errors were smaller for the INCUS filter than the uniform filter when either of these was used in combination with any of the other filters. The INCUS technique provides a straightforward, higher degree of freedom, and computationally feasible implementation of a general purpose de-noising filter for surface coil-based imaging including parallel imaging in commercial MR imaging.

Efficient Wiener filtering without preconditioning

We present a new approach to calculate the Wiener filter solution of general data sets. It is trivial to implement, flexible, numerically absolutely stable, and guaranteed to converge. Most importantly, it does not require an ingenious choice of preconditioner to work well. The method is capable of taking into account inhomogeneous noise distributions and arbitrary mask geometries. It iteratively builds up the signal reconstruction by means of a messenger field, introduced to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently. Using cosmic microwave background (CMB) radiation data as a showcase, we demonstrate the capabilities of our scheme by computing Wiener filtered WMAP7 temperature and polarization maps at full resolution for the first time. We show how the algorithm can be modified to synthesize fluctuation maps, which, combined with the Wiener filter solution, result in unbiased constrained signal realizations, consistent with the observations. The algorithm performs well even on simulated CMB maps with Planck resolution and dynamic range.