Showing papers on "Noise published in 2010"

Functional roles for noise in genetic circuits

Abstract: The genetic circuits that regulate cellular functions are subject to stochastic fluctuations, or ‘noise’, in the levels of their components. Noise, far from just a nuisance, has begun to be appreciated for its essential role in key cellular activities. Noise functions in both microbial and eukaryotic cells, in multicellular development, and in evolution. It enables coordination of gene expression across large regulons, as well as probabilistic differentiation strategies that function across cell populations. At the longest timescales, noise may facilitate evolutionary transitions. Here we review examples and emerging principles that connect noise, the architecture of the gene circuits in which it is present, and the biological functions it enables. We further indicate some of the important challenges and opportunities going forward.

Adaptive non‐local means denoising of MR images with spatially varying noise levels

Abstract: PURPOSE: To adapt the so-called nonlocal means filter to deal with magnetic resonance (MR) images with spatially varying noise levels (for both Gaussian and Rician distributed noise). MATERIALS AND METHODS: Most filtering techniques assume an equal noise distribution across the image. When this assumption is not met, the resulting filtering becomes suboptimal. This is the case of MR images with spatially varying noise levels, such as those obtained by parallel imaging (sensitivity-encoded), intensity inhomogeneity-corrected images, or surface coil-based acquisitions. We propose a new method where information regarding the local image noise level is used to adjust the amount of denoising strength of the filter. Such information is automatically obtained from the images using a new local noise estimation method. RESULTS: The proposed method was validated and compared with the standard nonlocal means filter on simulated and real MRI data showing an improved performance in all cases. CONCLUSION: The new noise-adaptive method was demonstrated to outperform the standard filter when spatially varying noise is present in the images.

The costs of chronic noise exposure for terrestrial organisms

Abstract: Growth in transportation networks, resource extraction, motorized recreation and urban development is responsible for chronic noise exposure in most terrestrial areas, including remote wilderness sites. Increased noise levels reduce the distance and area over which acoustic signals can be perceived by animals. Here, we review a broad range of findings that indicate the potential severity of this threat to diverse taxa, and recent studies that document substantial changes in foraging and anti-predator behavior, reproductive success, density and community structure in response to noise. Effective management of protected areas must include noise assessment, and research is needed to further quantify the ecological consequences of chronic noise exposure in terrestrial environments.

Stable Principal Component Pursuit

Abstract: In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex program, named Principal Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted by gross sparse errors. We further prove that the solution to a related convex program (a relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small entrywise noise and robust to gross sparse errors. More precisely, our result shows that the proposed convex program recovers the low-rank matrix even though a positive fraction of its entries are arbitrarily corrupted, with an error bound proportional to the noise level. We present simulation results to support our result and demonstrate that the new convex program accurately recovers the principal components (the low-rank matrix) under quite broad conditions. To our knowledge, this is the first result that shows the classical Principal Component Analysis (PCA), optimal for small i.i.d. noise, can be made robust to gross sparse errors; or the first that shows the newly proposed PCP can be made stable to small entry-wise perturbations.

Image Denoising Methods. A New Nonlocal Principle

Abstract: The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove fine structures in images. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise,” defined as the difference between a digital image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods is compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of $L^2$ distances of the denoised version to the original image. The fourth and perhaps most powerful evaluation method is, however, the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.

An Optimal Two-stage Identification Algorithm for Hammerstein―Wiener Nonlinear Systems

Abstract: An optimal two-stage identification algorithm is presented for Hammerstein–Wiener systems where two static nonlinear elements surround a linear block. The proposed algorithm consists of two steps: The first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases. Moreover, the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.

Automatic Parameter Selection for Denoising Algorithms Using a No-Reference Measure of Image Content

Abstract: Across the field of inverse problems in image and video processing, nearly all algorithms have various parameters which need to be set in order to yield good results. In practice, usually the choice of such parameters is made empirically with trial and error if no “ground-truth” reference is available. Some analytical methods such as cross-validation and Stein's unbiased risk estimate (SURE) have been successfully used to set such parameters. However, these methods tend to be strongly reliant on restrictive assumptions on the noise, and also computationally heavy. In this paper, we propose a no-reference metric Q which is based upon singular value decomposition of local image gradient matrix, and provides a quantitative measure of true image content (i.e., sharpness and contrast as manifested in visually salient geometric features such as edges,) in the presence of noise and other disturbances. This measure 1) is easy to compute, 2) reacts reasonably to both blur and random noise, and 3) works well even when the noise is not Gaussian. The proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms. Ample simulated and real data experiments support our claims. Furthermore, tests using the TID2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions.

Noise Adaptive Fuzzy Switching Median Filter for Salt-and-Pepper Noise Reduction

Abstract: This letter presents a novel two-stage noise adaptive fuzzy switching median (NAFSM) filter for salt-and-pepper noise detection and removal. Initially, the detection stage will utilize the histogram of the corrupted image to identify noise pixels. These detected ?noise pixels? will then be subjected to the second stage of the filtering action, while ?noise-free pixels? are retained and left unprocessed. Then, the NAFSM filtering mechanism employs fuzzy reasoning to handle uncertainty present in the extracted local information as introduced by noise. Simulation results indicate that the NAFSM is able to outperform some of the salt-and-pepper noise filters existing in literature.

A study of the effect of different types of noise on the precision of supervised learning techniques

Abstract: Machine learning techniques often have to deal with noisy data, which may affect the accuracy of the resulting data models. Therefore, effectively dealing with noise is a key aspect in supervised learning to obtain reliable models from data. Although several authors have studied the effect of noise for some particular learners, comparisons of its effect among different learners are lacking. In this paper, we address this issue by systematically comparing how different degrees of noise affect four supervised learners that belong to different paradigms. Specifically, we consider the Naive Bayes probabilistic classifier, the C4.5 decision tree, the IBk instance-based learner and the SMO support vector machine. We have selected four methods which enable us to contrast different learning paradigms, and which are considered to be four of the top ten algorithms in data mining (Yu et al. 2007). We test them on a collection of data sets that are perturbed with noise in the input attributes and noise in the output class. As an initial hypothesis, we assign the techniques to two groups, NB with C4.5 and IBk with SMO, based on their proposed sensitivity to noise, the first group being the least sensitive. The analysis enables us to extract key observations about the effect of different types and degrees of noise on these learning techniques. In general, we find that Naive Bayes appears as the most robust algorithm, and SMO the least, relative to the other two techniques. However, we find that the underlying empirical behavior of the techniques is more complex, and varies depending on the noise type and the specific data set being processed. In general, noise in the training data set is found to give the most difficulty to the learners.

Almost 40 Years of Airframe Noise Research: What Did We Achieve?

Abstract: With the advent of low noise high bypass ratio turbofan engines airframe noise gained significant importance with respect to the overall aircraft noise impact around airports. Already around 1970 airframe noise, originating from flow around the landing gears and high-lift devices, was recognized as a potential “lower aircraft noise barrier” at approach and landing. Since then, the outcome of extensive acoustic flight tests and aeroacoustic wind tunnel experiments enabled a detailed description and ranking of the major airframe noise sources and the development of noise reduction means. In the last decade advances in numerical and experimental tools led to a better understanding of complex noise source mechanisms. Efficient noise reduction technologies were developed for landing gears while the benefits of high-lift noise reduction means were often compensated by a simultaneous degradation in aerodynamic performance. The focus of this paper is not on the historical sequence of airframe noise research but rather aims to provide a concise survey of the achievements in airframe noise source description and reduction over the last 40 years worldwide. Due to the vast amount of work focused on a variety of airframe noise problems, this review can only provide examples but does not claim to be complete.

On Optimal Frequency-Domain Multichannel Linear Filtering for Noise Reduction

Abstract: Several contributions have been made so far to develop optimal multichannel linear filtering approaches and show their ability to reduce the acoustic noise. However, there has not been a clear unifying theoretical analysis of their performance in terms of both noise reduction and speech distortion. To fill this gap, we analyze the frequency-domain (non-causal) multichannel linear filtering for noise reduction in this paper. For completeness, we consider the noise reduction constrained optimization problem that leads to the parameterized multichannel non-causal Wiener filter (PMWF). Our contribution is fivefold. First, we formally show that the minimum variance distortionless response (MVDR) filter is a particular case of the PMWF by properly formulating the constrained optimization problem of noise reduction. Second, we propose new simplified expressions for the PMWF, the MVDR, and the generalized sidelobe canceller (GSC) that depend on the signals' statistics only. In contrast to earlier works, these expressions are explicitly independent of the channel transfer function ratios. Third, we quantify the theoretical gains and losses in terms of speech distortion and noise reduction when using the PWMF by establishing new simplified closed-form expressions for three performance measures, namely, the signal distortion index, the noise reduction factor (originally proposed in the paper titled ldquoNew insights into the noise reduction Wiener filter,rdquo by J. Chen (IEEE Transactions on Audio, Speech, and Language Processing, Vol. 15, no. 4, pp. 1218-1234, Jul. 2006) to analyze the single channel time-domain Wiener filter), and the output signal-to-noise ratio (SNR). Fourth, we analyze the effects of coherent and incoherent noise in addition to the benefits of utilizing multiple microphones. Fifth, we propose a new proof for the a posteriori SNR improvement achieved by the PMWF. Finally, we provide some simulations results to corroborate the findings of this work.

Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization

Abstract: Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: (1) converting the multiplicative model into an additive one by taking logarithms, as proposed by some other authors; (2) using variable splitting to obtain an equivalent constrained problem; and (3) dealing with this optimization problem using the augmented Lagrangian framework. A set of experiments shows that the proposed method, which we name MIDAL (multiplicative image denoising by augmented Lagrangian), yields state-of-the-art results both in terms of speed and denoising performance.

Acoustic Territories: Sound Culture and Everyday Life

Abstract: Introduction: your sound is my sound is your sound 1. Underground: Busking, Acousmatics, and the Echo 2. Home: Ethical Volumes of Silence and Noise 3. Sidewalk: Steps, Gait, and Rhythmic Journey-Forms 4. Street: Auditory Latching, Cars, and the Dynamics of Vibration 5. Shopping Mall: Muzak, Mishearing, and the Productive Volatility of Feedback 6. Sky: Radio, Spatial Urbanism, and Cultures of Transmission Bibliography Index.

Channel coding: non-asymptotic fundamental limits

Abstract: Noise is an inalienable property of all communication systems appearing in nature. Such noise acts against the very purpose of communication, that is delivery of a data to the destination with minimal possible distortion. This creates a problem that has been addressed by various disciplines over the past century. In particular, information theory studies the question of the maximum possible rate achievable by an ideal system under certain assumptions regarding the noise generation and structural design constraints. The study of such questions, initiated by Claude Shannon in 1948, has typically been carried out in the asymptotic limit of an infinite number of signaling degrees of freedom (blocklength). Such a regime corresponds to the regime of laws of large numbers, or more generally ergodic limits, in probability theory. However, with the ever increasing demand for ubiquitous access to real time data, such as audio and video streaming for mobile devices, as well as the advent of modern sparse graph codes, one is interested in describing fundamental limits non-asymptotically, i.e. for blocklengths of the order of 1000. Study of these practically motivated questions requires new tools and techniques, which are systematically developed in this work. Knowledge of the behavior of the fundamental limits in the non-asymptotic regime enables the analysis of many related questions, such as the energy efficiency, effects of dynamically varying channel state, assessment of the suboptimality of modern codes, benefits of feedback, etc. As a result it is discovered that in several instances classical (asymptotics-based) conclusions do not hold under this more refined approach.

NoiseSPY: A Real-Time Mobile Phone Platform for Urban Noise Monitoring and Mapping

Abstract: In this paper we present the design, implementation, evaluation, and user experiences of the NoiseSpy application, our sound sensing system that turns the mobile phone into a low-cost data logger for monitoring environmental noise. It allows users to explore a city area while collaboratively visualizing noise levels in real-time. The software combines the sound levels with GPS data in order to generate a map of sound levels that were encountered during a journey. We report early findings from the trials which have been carried out by cycling couriers who were given Nokia mobile phones equipped with the NoiseSpy software to collect noise data around Cambridge city. Indications are that, not only is the functionality of this personal environmental sensing tool engaging for users, but aspects such as personalization of data, contextual information, and reflection upon both the data and its collection, are important factors in obtaining and retaining their interest.

Conducted EMI Mitigation Techniques for Switch-Mode Power Converters: A Survey

Abstract: Several techniques to mitigate conducted electromagnetic interference (EMI) in switch-mode power supplies (SMPS) have been reported in literature. Of these, this paper reviews those techniques that are primarily meant for ac-dc and dc-dc power converters. The techniques are broadly classified based on two criteria-1) reduction of the noise after generation and 2) reduction of the noise at the generation stage itself. A detailed classification and review of various noise mitigation techniques currently available in literature are presented. It is believed that the classification and review of the conducted EMI mitigation techniques presented in this paper would be useful to SMPS researchers and designers.

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

Abstract: In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer for removing multiplicative Gamma noise. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizers of our restoration functionals by applying Douglas-Rachford splitting techniques, resp. alternating direction methods of multipliers. For a particular splitting, we present a semi-implicit scheme to solve the involved nonlinear systems of equations and prove its Q-linear convergence. Finally, we demonstrate the performance of our methods by numerical examples.

MMSE based noise PSD tracking with low complexity

Abstract: Most speech enhancement algorithms heavily depend on the noise power spectral density (PSD). Because this quantity is unknown in practice, estimation from the noisy data is necessary. We present a low complexity method for noise PSD estimation. The algorithm is based on a minimum mean-squared error estimator of the noise magnitude-squared DFT coefficients. Compared to minimum statistics based noise tracking, segmental SNR and PESQ are improved for non-stationary noise sources with 1 dB and 0.25 MOS points, respectively. Compared to recently published algorithms, similar good noise tracking performance is obtained, but at a computational complexity that is in the order of a factor 40 lower.

Analytical Model for Predicting Noise and Vibration in Permanent-Magnet Synchronous Motors

Abstract: This paper analyzes the noise and vibration in permanent-magnet synchronous motors (PMSMs). Electromagnetic forces have been identified as the main cause of noise and vibration in these machines, rather than the torque ripple and cogging torque. A procedure for calculating the magnetic forces on the stator teeth based on the 2-D finite-element (FE) method is presented first. An analytical model is then developed to predict the radial displacement along the stator teeth. The displacement calculations from the analytical model are validated with structural finite-element analysis (FEA) and experimental data. Finally, the radial displacement is converted into sound power level. Four different PMSM topologies, suitable for the electric power steering application, are compared for their performances with regard to noise and vibration.

Subspace-Based Optimization Method for Solving Inverse-Scattering Problems

Abstract: This paper investigates a modified version of the subspace-based optimization method for solving inverse-scattering problems The method is found to share several properties with the contrast-source-inversion method The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the rest is determined by optimization method This feature significantly speeds up the convergence of the algorithm There is a great flexibility in partitioning the space of induced current into two orthogonal complementary subspaces: the signal subspace and the noise subspace This flexibility enables the algorithm to perform robustly against noise Numerical simulations validate the efficacy of the proposed method: fast convergent and robust against noise

Characterizing the Influence of System Noise on Large-Scale Applications by Simulation

Abstract: This paper presents an in-depth analysis of the impact of system noise on large-scale parallel application performance in realistic settings. Our analytical model shows that not only collective operations but also point-to-point communications influence the application's sensitivity to noise. We present a simulation toolchain that injects noise delays from traces gathered on common large-scale architectures into a LogGPS simulation and allows new insights into the scaling of applications in noisy environments. We investigate collective operations with up to 1 million processes and three applications (Sweep3D, AMG, and POP) with up to 32,000 processes.We show that the scale at which noise becomes a bottleneck is system-specific and depends on the structure of the noise. Simulations with different network speeds show that a 10x faster network does not improve application scalability. We quantify noise and conclude that our tools can be utilized to tune the noise signatures of a specific system.

Participatory noise pollution monitoring using mobile phones

Abstract: Noise pollution is a major problem in cities around the world The current methods to assess it neglect to represent the real exposure experienced by the citizens themselves, and therefore could lead to wrong conclusions and a biased representations In this paper we present a novel approach to monitor noise pollution involving the general public Using their mobile phones as noise sensors, we provide a low cost solution for the citizens to measure their personal exposure to noise in their everyday environment and participate in the creation of collective noise maps by sharing their geo-localized and annotated measurements with the community Our prototype, called NoiseTube, can be found online [1]

Perceptual assessment of quality of urban soundscapes with combined noise sources and water sounds

Abstract: In this study, urban soundscapes containing combined noise sources were evaluated through field surveys and laboratory experiments. The effect of water sounds on masking urban noises was then examined in order to enhance the soundscape perception. Field surveys in 16 urban spaces were conducted through soundwalking to evaluate the annoyance of combined noise sources. Synthesis curves were derived for the relationships between noise levels and the percentage of highly annoyed (%HA) and the percentage of annoyed (%A) for the combined noise sources. Qualitative analysis was also made using semantic scales for evaluating the quality of the soundscape, and it was shown that the perception of acoustic comfort and loudness was strongly related to the annoyance. A laboratory auditory experiment was then conducted in order to quantify the total annoyance caused by road traffic noise and four types of construction noise. It was shown that the annoyance ratings were related to the types of construction noise in combination with road traffic noise and the level of the road traffic noise. Finally, water sounds were determined to be the best sounds to use for enhancing the urban soundscape. The level of the water sounds should be similar to or not less than 3 dB below the level of the urban noises.

Orientation Estimation Using a Quaternion-Based Indirect Kalman Filter With Adaptive Estimation of External Acceleration

Abstract: This paper is concerned with orientation estimation using inertial and magnetic sensors. A quaternion-based indirect Kalman filter structure is used. The magnetic sensor output is only used for yaw angle estimation using two-step measurement updates. External acceleration is estimated from the residual of the filter and compensated by increasing the measurement noise covariance. Using the direction information of external information, the proposed method prevents unnecessarily increasing the measurement noise covariance corresponding to the accelerometer output, which is not affected by external acceleration. Through numerical examples, the proposed method is verified.

Load Signature Study—Part II: Disaggregation Framework, Simulation, and Applications

Abstract: Load signatures embedded in common electricity consumption patterns, in fact, could render much information pertaining to the nature of the appliances and their usage patterns. Based on the proposed disaggregation framework, we use three advanced disaggregation algorithms, called committee decision mechanisms (CDMs), to perform load disaggregation at the metering level. Three random switching simulators are also developed to investigate the performance of different CDMs under a variety of scenarios. Through Monte Carlo simulations, we demonstrate that all CDMs outperform any single-feature, single-algorithm-based disaggregation methods. With sensitivity analysis, we also show that the CDMs are less sensitive to any load dynamics and noise. We finally demonstrate some applications of this technology in terms of appliance usage tacking and estimated energy consumption of each appliance.

Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves

Abstract: We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as 1/f γ. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the mid-transit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for mid-transit times and truer estimates of their uncertainties.

Optimal HDR reconstruction with linear digital cameras

Abstract: Given a multi-exposure sequence of a scene, our aim is to recover the absolute irradiance falling onto a linear camera sensor. The established approach is to perform a weighted average of the scaled input exposures. However, there is no clear consensus on the appropriate weighting to use. We propose a weighting function that produces statistically optimal estimates under the assumption of compound-Gaussian noise. Our weighting is based on a calibrated camera model that accounts for all noise sources. This model also allows us to simultaneously estimate the irradiance and its uncertainty. We evaluate our method on simulated and real world photographs, and show that we consistently improve the signal-to-noise ratio over previous approaches. Finally, we show the effectiveness of our model for optimal exposure sequence selection and HDR image denoising.

Noise and signal properties in PSF-based fully 3D PET image reconstruction: an experimental evaluation

Abstract: The addition of accurate system modeling in PET image reconstruction results in images with distinct noise texture and characteristics. In particular, the incorporation of point spread functions (PSF) into the system model has been shown to visually reduce image noise, but the noise properties have not been thoroughly studied. This work offers a systematic evaluation of noise and signal properties in different combinations of reconstruction methods and parameters. We evaluate two fully 3D PET reconstruction algorithms: (1) OSEM with exact scanner line of response modeled (OSEM+LOR), (2) OSEM with line of response and a measured point spread function incorporated (OSEM+LOR+PSF), in combination with the effects of four post-reconstruction filtering parameters and 1-10 iterations, representing a range of clinically acceptable settings. We used a modified NEMA image quality (IQ) phantom, which was filled with 68Ge and consisted of six hot spheres of different sizes with a target/background ratio of 4:1. The phantom was scanned 50 times in 3D mode on a clinical system to provide independent noise realizations. Data were reconstructed with OSEM+LOR and OSEM+LOR+PSF using different reconstruction parameters, and our implementations of the algorithms match the vendor's product algorithms. With access to multiple realizations, background noise characteristics were quantified with four metrics. Image roughness and the standard deviation image measured the pixel-to-pixel variation; background variability and ensemble noise quantified the region-to-region variation. Image roughness is the image noise perceived when viewing an individual image. At matched iterations, the addition of PSF leads to images with less noise defined as image roughness (reduced by 35% for unfiltered data) and as the standard deviation image, while it has no effect on background variability or ensemble noise. In terms of signal to noise performance, PSF-based reconstruction has a 7% improvement in contrast recovery at matched ensemble noise levels and 20% improvement of quantitation SNR in unfiltered data. In addition, the relations between different metrics are studied. A linear correlation is observed between background variability and ensemble noise for all different combinations of reconstruction methods and parameters, suggesting that background variability is a reasonable surrogate for ensemble noise when multiple realizations of scans are not available.