Inhomogeneous Noise Research Articles

The Simons Observatory: Combining cross-spectral foreground cleaning with multitracer B -mode delensing for improved constraints on inflation

The Simons Observatory (SO), due to start full science operations in early 2025, aims to set tight constraints on inflationary physics by inferring the tensor-to-scalar ratio r from measurements of cosmic microwave background (CMB) polarization B-modes. Its nominal design including three small-aperture telescopes (SATs) targets a precision σ(r=0)≤0.003 without delensing. Achieving this goal and further reducing uncertainties requires a thorough understanding and mitigation of other large-scale B-mode sources such as Galactic foregrounds and weak gravitational lensing. We present an analysis pipeline aiming to estimate r by including delensing within a cross-spectral likelihood, and demonstrate it for the first time on SO-like simulations accounting for various levels of foreground complexity, inhomogeneous noise and partial sky coverage. As introduced in an earlier SO delensing paper, lensing B-modes are synthesized using internal CMB lensing reconstructions as well as -like cosmic infrared background maps and LSST-like galaxy density maps. We then extend SO’s power-spectrum-based foreground-cleaning algorithm to include all auto- and cross-spectra between the lensing template and the SAT B-modes in the likelihood function. This allows us to constrain r and the parameters of our foreground model simultaneously. Within this framework, we demonstrate the equivalence of map-based and cross-spectral delensing and use it to motivate an optimized pixel-weighting scheme for power spectrum estimation. We start by validating our pipeline in the simplistic case of uniform foreground spectral energy distributions. In the absence of primordial B-modes, we find that the 1σ statistical uncertainty on r, σ(r), decreases by 37% as a result of delensing. Tensor modes at the level of r=0.01 are successfully detected by our pipeline. Even when using more realistic foreground models including spatial variations in the dust and synchrotron spectral properties, we obtain unbiased estimates of r both with and without delensing by employing the moment-expansion method. In this case, uncertainties are increased due to the higher number of model parameters, and delensing-related improvements range between 27% and 31%. These results constitute the first realistic assessment of the delensing performance at SO’s nominal sensitivity level. Published by the American Physical Society 2024

Identifying cell states in single-cell RNA-seq data at statistically maximal resolution.

Single-cell RNA sequencing (scRNA-seq) has become a popular experimental method to study variation of gene expression within a population of cells. However, obtaining an accurate picture of the diversity of distinct gene expression states that are present in a given dataset is highly challenging because of the sparsity of the scRNA-seq data and its inhomogeneous measurement noise properties. Although a vast number of different methods is applied in the literature for clustering cells into subsets with 'similar' expression profiles, these methods generally lack rigorously specified objectives, involve multiple complex layers of normalization, filtering, feature selection, dimensionality-reduction, employ ad hoc measures of distance or similarity between cells, often ignore the known measurement noise properties of scRNA-seq measurements, and include a large number of tunable parameters. Consequently, it is virtually impossible to assign concrete biophysical meaning to the clusterings that result from these methods. Here we address the following problem: Given raw unique molecule identifier (UMI) counts of an scRNA-seq dataset, partition the cells into subsets such that the gene expression states of the cells in each subset are statistically indistinguishable, and each subset corresponds to a distinct gene expression state. That is, we aim to partition cells so as to maximally reduce the complexity of the dataset without removing any of its meaningful structure. We show that, given the known measurement noise structure of scRNA-seq data, this problem is mathematically well-defined and derive its unique solution from first principles. We have implemented this solution in a tool called Cellstates which operates directly on the raw data and automatically determines the optimal partition and cluster number, with zero tunable parameters. We show that, on synthetic datasets, Cellstates almost perfectly recovers optimal partitions. On real data, Cellstates robustly identifies subtle substructure within groups of cells that are traditionally annotated as a common cell type. Moreover, we show that the diversity of gene expression states that Cellstates identifies systematically depends on the tissue of origin and not on technical features of the experiments such as the total number of cells and total UMI count per cell. In addition to the Cellstates tool we also provide a small toolbox of software to place the identified cellstates into a hierarchical tree of higher-order clusters, to identify the most important differentially expressed genes at each branch of this hierarchy, and to visualize these results.

The Simons Observatory: Pipeline comparison and validation for large-scale B-modes

Context. The upcoming Simons Observatory Small Aperture Telescopes aim at achieving a constraint on the primordial tensor-to-scalar ratio r at the level of σ(r = 0)≲0.003, observing the polarized CMB in the presence of partial sky coverage, cosmic variance, inhomogeneous non-white noise, and Galactic foregrounds. Aims. We present three different analysis pipelines able to constrain r given the latest available instrument performance, and compare their predictions on a set of sky simulations that allow us to explore a number of Galactic foreground models and elements of instrumental noise, relevant for the Simons Observatory. Methods. The three pipelines employ different combinations of parametric and non-parametric component separation at the map and power spectrum levels, and use B-mode purification to estimate the CMB B-mode power spectrum. We applied them to a common set of simulated realistic frequency maps, and compared and validated them with focus on their ability to extract robust constraints on the tensor-to-scalar ratio r. We evaluated their performance in terms of bias and statistical uncertainty on this parameter. Results. In most of the scenarios the three methodologies achieve similar performance. Nevertheless, several simulations with complex foreground signals lead to a > 2σ bias on r if analyzed with the default versions of these pipelines, highlighting the need for more sophisticated pipeline components that marginalize over foreground residuals. We show two such extensions, using power-spectrum-based and map-based methods, that are able to fully reduce the bias on r below the statistical uncertainties in all foreground models explored, at a moderate cost in terms of σ(r).

Enhancing CMB map reconstruction and power spectrum estimation with convolutional neural networks

The accurate reconstruction of Cosmic Microwave Background (CMB) maps and the measurement of its power spectrum are crucial for studying the early universe. In this paper, we implement a convolutional neural network to apply the Wiener Filter to CMB temperature maps, and use it intensively to compute an optimal quadratic estimation of the power spectrum. Our neural network has a UNet architecture as that implemented in WienerNet, but with novel aspects such as being written in python 3 and TensorFlow 2. It also includes an extra channel for the noise variance map, to account for inhomogeneous noise, and a channel for the mask. The network is very efficient, overcoming the bottleneck that is typically found in standard methods to compute the Wiener Filter, such as those that apply the conjugate gradient. It scales efficiently with the size of the map, making it a useful tool to include in CMB data analysis. The accuracy of the Wiener Filter reconstruction is satisfactory, as compared with the standard method. We heavily use this approach to efficiently estimate the power spectrum, by performing a simulation-based analysis of the optimal quadratic estimator. We further evaluate the quality of the reconstructed maps in terms of the power spectrum and find that we can properly recover the statistical properties of the signal. We find that the proposed architecture can account for inhomogeneous noise efficiently. Furthermore, increasing the complexity of the variance map presents a more significant challenge for the convergence of the network than the noise level does.

CMB-S4: Iterative Internal Delensing and r Constraints

The tightest constraints on the tensor-to-scalar ratio r can only be obtained after removing a substantial fraction of the lensing B-mode sample variance. The planned Cosmic Microwave Background (CMB)-S4 experiment (cmb-s4.org) will remove the lensing B-mode signal internally by reconstructing the gravitational lenses from high-resolution observations. We document here a first lensing reconstruction pipeline able to achieve this optimally for arbitrary sky coverage. We make it part of a map-based framework to test CMB-S4 delensing performance and its constraining power on r, including inhomogeneous noise and two non-Gaussian Galactic polarized foreground models. The framework performs component separation of the high-resolution maps, followed by the construction of lensing B-mode templates, which are then included in a parametric small-aperture map cross-spectra-based likelihood for r. We find that the lensing reconstruction and framework achieve the expected performance, compatible with the target σ(r) ≃ 5 · 10−4 in the absence of a tensor signal, after an effective removal of 92%–93% of the lensing B-mode variance, depending on the simulation set. The code for the lensing reconstruction can also be used for cross-correlation studies with large-scale structures, lensing spectrum reconstruction, cluster lensing, or other CMB lensing-related purposes. As part of our tests, we also demonstrate the joint optimal reconstruction of the lensing potential with the lensing curl potential mode at second order in the density fluctuations.

Self-supervised dual-domain balanced dropblock-network for low-dose CT denoising

Objective. Self-supervised learning methods have been successfully applied for low-dose computed tomography (LDCT) denoising, with the advantage of not requiring labeled data. Conventional self-supervised methods operate only in the image domain, ignoring valuable priors in the sinogram domain. Recently proposed dual-domain methods address this limitation but encounter issues with blurring artifacts in the reconstructed image due to the inhomogeneous distribution of noise levels in low-dose sinograms. Approach. To tackle this challenge, this paper proposes SDBDNet, an end-to-end dual-domain self-supervised method for LDCT denoising. With the network designed based on the properties of inhomogeneous noise in low-dose sinograms and the principle of moderate sinogram-domain denoising, SDBDNet achieves effective denoising in dual domains without introducing blurring artifacts. Specifically, we split the sinogram into two subsets based on the positions of detector cells to generate paired training data with high similarity and independent noise. These sub-sinograms are then restored to their original size using 1D interpolation and learning-based correction. To achieve adaptive and moderate smoothing in the sinogram domain, we integrate Dropblock, a type of convolution layer with regularization, into SDBDNet, and set a weighted average between the denoised sinograms and their noisy counterparts, leading to a well-balanced dual-domain approach. Main results. Numerical experiments show that our method outperforms popular non-learning and self-supervised learning methods, demonstrating its effectiveness and superior performance. Significance. While introducing a novel high-performance dual-domain self-supervised LDCT denoising method, this paper also emphasizes and verifies the importance of appropriate sinogram-domain denoising in dual-domain methods, which might inspire future work.

Directed mean curvature flow in noisy environment

AbstractWe consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole–Hopf solution of the KPZ equation. This result follows from the analysis of a more general system of nonlinear SPDEs driven by inhomogeneous noises, using the theory of regularity structures. However, due to inhomogeneity of the noise, the “black box” result developed in the series of works cannot be applied directly and requires significant extension to infinite‐dimensional regularity structures. Analysis of this general system of SPDEs gives two more interesting results. First, we prove that the solution of the quenched KPZ equation with a very strong force also converges to the Cole–Hopf solution of the KPZ equation. Second, we show that a properly rescaled and renormalised quenched Edwards–Wilkinson model in any dimension converges to the stochastic heat equation.

Solving a nonlinear fractional SPDE with spatially inhomogeneous white noise

In this paper, we study the following nonlinear fractional stochastic partial differential equation where denotes the Markovian generator of a stable-like Feller process with variable order and is a measurable function. The forcing noise denoted by is a spatially inhomogeneous white noise. Under some assumptions on the catalytic measure of the inhomogeneous Brownian sheet , we study the moment bounds for the solution. As a byproduct, we prove that the solution is weakly full intermittent based on the moment estimates of the solution. We also study the Hölder regularity of the solution with respect to the temporal and spatial variables, respectively.

Data-Augmented Manifold Learning Thermography for Defect Detection and Evaluation of Polymer Composites.

Infrared thermography techniques with thermographic data analysis have been widely applied to non-destructive tests and evaluations of subsurface defects in practical composite materials. However, the performance of these methods is still restricted by limited informative images and difficulties in feature extraction caused by inhomogeneous backgrounds and noise. In this work, a novel generative manifold learning thermography (GMLT) is proposed for defect detection and the evaluation of composites. Specifically, the spectral normalized generative adversarial networks serve as an image augmentation strategy to learn the thermal image distribution, thereby generating virtual images to enrich the dataset. Subsequently, the manifold learning method is employed for the unsupervised dimensionality reduction in all images. Finally, the partial least squares regression is presented to extract the explicit mapping of manifold learning for defect visualization. Moreover, probability density maps and quantitative metrics are proposed to evaluate and explain the obtained defect detection performance. Experimental results on carbon fiber-reinforced polymers demonstrate the superiorities of GMLT, compared with other methods.

Evolution systems and continuity equations for white noise functionals

In this paper, by applying the quantum decomposition of white noise functionals, the continuity equations for white noise functionals are reformulated as time inhomogeneous white noise differential equations. We establish a systematic study of the evolution systems whose infinitesimal generators are quadratic quantum white noises and then, as an application, we study the continuity equations for white noise functionals of which the coefficient has up to the first chaos (Gaussian process). The restriction for the coefficient is comparable (not necessarily equivalent) to the integrability condition of the exponential of the coefficient by Ambrosio and Figalli [J. Funct. Anal. 256, 179–214 (2009)] for the well-posedness of the continuity equation in the abstract Wiener space setting.

Directional and seasonal variations of seismic ambient noise in southeastern Canada and the NE USA

SUMMARY Ambient seismic noise is mainly generated in oceans through the interactions between the atmosphere, ocean waves and the solid Earth. Study areas located near the edges of continents are thus subject to receiving an inhomogeneous noise field that could cause bias in ambient noise wave attenuation measurements and tomography studies. Ambient seismic noise characteristics across SE Canada and the NE USA are studied in detail at a regional scale for the first time, due to the availability of over 2 yr of data (2013–2015) recorded at 69 broad-band seismographs. This large, dense data set allowed us to use a back-projection technique to investigate both the azimuthal and temporal variations of the ambient noise. This method is based on a statistical analysis of signal-to-noise ratios (SNRs) of the waveforms in the calculated empirical Green’s functions for pairs of stations. We propose a new method of analysing the SNR by modifying the already existing concept of fan diagrams to include both causal and acausal components of the noise cross-correlograms in the analysis. We investigate directional and seasonal variations of the recorded noise data across the study area at the three main passbands of the seismic noise spectrum including the secondary microseisms (SM; 3–10 s), the primary microseisms (PM; 10–30 s), and the seismic hum (Hum; 30–300 s). We observe that the strongest and weakest signals are received at the SM and Hum bands, respectively. Considering the results of this study along with those from previous studies, we conclude that the strongest seismic noise arrivals at the three passbands investigated in this study (i.e. SM, PM and Hum) are generated at different locations in the Atlantic, Pacific and Arctic oceans.

Enhanced Phase Noise Reduction in Localized Two-Way Optical Frequency Comparison

High-stability optical frequency comparison over fiber link enables the establishment of ultrastable optical clock networks, having the potential to promote a series of applications, including metrology, geodesy, and astronomy. In this article, we theoretically analyze and experimentally demonstrate a timedelayed local two-way (TD-LTW) optical frequency comparison scheme with improved comparison stability, showing that the fractional instability of optical frequency comparison over a 50- km transfer link can be reduced from $1.30\times10^{-15}$ to $5.25\times10^{-16}$ at the 1 s integration time with an improvement factor of 2.48. Additionally, we also for the first time model and experimentally verify the effect of the inhomogeneous phase noise along the fiber link on the system performance. We believe that the theory and technique proposed here will be helpful in developing the high-stability optical clock networks over large-area fiber links.

Thermoelectric phenomena in a one-dimensional diffusive quantum medium

The quantum diffusion in a one-dimensional lattice in a tunneling regime under the influence of spatially inhomogeneous Gaussian noise is studied theoretically. It is shown that the thermopower appears at an arbitrary value of the tunneling coupling. In the strong tunneling regime at an extremely high temperature, when the drift component of the charge transport can be neglected, the thermoelectric effect takes place only in the presence of a constant external electric field. The Seebeck and Peltier coefficients for the closed-circuit mode are obtained for a one-dimensional quantum diffusion medium in the tunneling regime. In the strong tunneling regime, both the thermopower and the Peltier effect are essentially nonlinear phenomena.

Effects of boosting on extragalactic components: methods and statistical studies

ABSTRACT In this work, we examine the impact of our motion with respect to the Cosmic Microwave Background (CMB) rest frame on statistics of CMB maps by examining the one-, two-, three-, and four- point statistics of simulated maps of the CMB and Sunyaev–Zeldovich (SZ) effects. We validate boosting codes by comparing their outcomes for temperature and polarization power spectra up to ℓ ≃ 6000. We derive and validate a new analytical formula for the computation of the boosted power spectrum of a signal with a generic frequency dependence. As an example we show how this increases the boosting correction to the power spectrum of CMB intensity measurements by ${\sim}30{{\ \rm per\ cent}}$ at 150 GHz. We examine the effect of boosting on thermal and kinetic SZ power spectra from semianalytical and hydrodynamical simulations; the boosting correction is generally small for both simulations, except when considering frequencies near the tSZ null. For the non-Gaussian statistics, in general we find that boosting has no impact with two exceptions. We find that, whilst the statistics of the CMB convergence field are unaffected, quadratic estimators that are used to measure this field can become biased at the $O(1){{\ \rm per\ cent}}$ level by boosting effects. We present a simple modification to the standard estimators that removes this bias. Second, bispectrum estimators can receive a systematic bias from the Doppler induced quadrupole when there is anisotropy in the sky – in practice this anisotropy comes from masking and inhomogeneous noise. This effect is unobservable and already removed by existing analysis methods.

The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors

Quantum walks are an analog of classical random walks in quantum systems. Quantum walks have smaller hitting times compared to classical random walks on certain types of graphs, leading to a quantum advantage of quantum-walks-based algorithms. An important feature of quantum walks is that they are accompanied by the excitation transfer from one site to another, and a moment of hitting the destination site is characterized by the maximum probability amplitude of observing the excitation on this site. It is therefore prospective to consider such problems as candidates for quantum advantage demonstration, since gate errors can smear out a peak in the transfer probability as a function of time, nevertheless leaving it distinguishable. We investigate the influence of quantum noise on hitting time and fidelity of a typical quantum walk problem - a perfect state transfer (PST) over a qubit chain. We simulate dynamics of a single excitation over the chain of qubits in the presence of typical noises of a quantum processor (homogeneous and inhomogeneous Pauli noise, crosstalk noise, thermal relaxation, and dephasing noise). We find that Pauli noise mostly smears out a peak in the fidelity of excitation transfer, while crosstalks between qubits mostly affect the hitting time. Knowledge about these noise patterns allows us to propose an error mitigation procedure, which we use to refine the results of running the PST on a simulator of a noisy quantum processor.

Morphology of weak lensing convergence maps

ABSTRACT We study the morphology of convergence maps by perturbatively reconstructing their Minkowski functionals (MFs). We present a systematic study using a set of three generalized skew spectra as a function of source redshift and smoothing angular scale. These spectra denote the leading-order corrections to the Gaussian MFs in the quasi-linear regime. They can also be used as independent statistics to probe the bispectrum. Using an approach based on pseudo-Sℓs, we show how these spectra will allow the reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the-art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics ℓ and source redshift zs, which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from cosmic microwave background observations, and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins.

Cosmic shear power spectra in practice

Cosmic shear is one of the most powerful probes of Dark Energy, targeted by several current and future galaxy surveys. Lensing shear, however, is only sampled at the positions of galaxies with measured shapes in the catalog, making its associated sky window function one of the most complicated amongst all projected cosmological probes of inhomogeneities, as well as giving rise to inhomogeneous noise. Partly for this reason, cosmic shear analyses have been mostly carried out in real-space, making use of correlation functions, as opposed to Fourier-space power spectra. Since the use of power spectra can yield complementary information and has numerical advantages over real-space pipelines, it is important to develop a complete formalism describing the standard unbiased power spectrum estimators as well as their associated uncertainties. Building on previous work, this paper contains a study of the main complications associated with estimating and interpreting shear power spectra, and presents fast and accurate methods to estimate two key quantities needed for their practical usage: the noise bias and the Gaussian covariance matrix, fully accounting for survey geometry, with some of these results also applicable to other cosmological probes. We demonstrate the performance of these methods by applying them to the latest public data releases of the Hyper Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence of systematics in our measurements and the validity of the covariance matrix estimate. We make the resulting power spectra, covariance matrices, null tests and all associated data necessary for a full cosmological analysis publicly available.

Active contour driven by adaptively weighted signed pressure force combined with Legendre polynomial for image segmentation

This paper proposes an active contour driven by adaptively weighted signed pressure force (SPF) combined with the Legendre polynomial method for image segmentation. First, an adaptively weighted global average intensity (GAI) term is defined wherein GAI differences are the weighted factors of the interior and exterior region-driving centers. Second, an adaptively weighted Legendre polynomial intensity (LPI) term is defined which adopts the Legendre polynomial intensity average differences as the weighted factors of the interior and exterior region-driving centers. Finally, the GAI and LPI terms are introduced into a novel SPF function and a coefficient is applied to weight their effect degrees; a new edge stopping function (ESF) is defined and combined with the region-based method to robustly converge the curve to the boundary of the object. Experiments demonstrate that this method is highly accurate and computationally efficient for images with inhomogeneous intensity, blurred edge, low contrast, and noise problems. Moreover, the segmentation results are independent of the initial contour.

DuroNet

Urban crime is an ongoing problem in metropolitan development and attracts general concern from the international community. As an effective means of defending urban safety, crime prediction plays a crucial role in patrol force allocation and public safety. However, urban crime data is a macro result of crime patterns overlapped by various irrelevant factors that cause inhomogeneous noises—local outliers and irregular waves. These noises might obstruct the learning process of crime prediction models and result in a deviation of performance. To tackle the problem, we propose a novel paradigm of <underline>Du</underline>al-<underline>ro</underline>bust Enhanced Spatial-temporal Learning <underline>Net</underline>work (DuroNet), an encoder-decoder architecture that possesses an adaptive robustness for reducing the effect of outliers and waves. The robustness is mainly reflected on two aspects. One is a locality enhanced module that employs local temporal context information to smooth the deviation of outliers and dynamic spatial information to assist in understanding normal points. The other is a self-attention-based pattern representation module to weaken the effect of irregular waves by learning attentive weights. Finally, extensive experiments are conducted on two real-world crime datasets before and after adding Gaussian noises. The results demonstrate the superior performance of our DuroNet over the state-of-the-art methods.

Introducing Swish and Parallelized Blind Removal Improves the Performance of a Convolutional Neural Network in Denoising MR Images.

PurposeTo improve the performance of a denoising convolutional neural network (DnCNN) and to make it applicable to images with inhomogeneous noise, a refinement involving an activation function (AF) and an application of the refined method for inhomogeneous-noise images was examined in combination with parallelized image denoising.MethodsImprovements in the DnCNN were performed by three approaches. One is refinement of the AF of each neural network that constructs the DnCNN. Swish was used in the DnCNN instead of rectifier linear unit. Second, blind noise removal was introduced to the DnCNN in order to adapt spatially variant noises. Third, blind noise removal was applied to parallelized image denoising, referred to herein as ParBID. The ParBID procedure is as follows: (1) adjacent 2D slice images are linearly combined to obtained higher peak SNR (PSNR) images, (2) combined images with different weight coefficients are denoised using the blind DnCNN, and (3) denoised combined images are separated into original position images by algebraic calculation.ResultsExperimental studies showed that the PSNR and the structural similarity index (SSIM) were improved by using Swish for all noise levels, from 2.5% to 7.5%, as compared to the conventional DnCNN. It was also shown that a well-trained CNN could remove spatially variant noises superimposed on images. Experimental studies with ParBID showed that the greatest PSNR and SSIM improvements were obtained at the middle slice when three slice images were used for linear image combination. More fine structures of images and image contrast remained when the proposed ParBID procedure was used.ConclusionSwish can improve the denoising performance of the DnCNN, and the denoising performance and effectiveness were further improved by ParBID.