Noise Conditions Research Articles

Elucidation of FDG-PET Imaging Characteristics that Reflect the Heterogeneity within Tumors Due to Variability in Metabolic Activity: A Phantom Study

Abstract Objective Focusing on the heterogeneity within cancer lesions and revealing cancer lesions with a high signal-to-noise ratio will help improve the quality of positron emission tomography (PET) images. This study aimed to understand how glucose metabolic activity can be shown with less statistical noise using a quality assessment phantom modeled after cancer lesions with a two-layer structure and a Clear adaptive Low-noise Method (CaLM) filter. Materials and Methods A National Electrical Manufacturers Association phantom with two spheres with a two-layer structure filled with 2-deoxy-2[18F]fluoro-D-glucose (inner and outer diameters of the spheres were 13/22 and 22/37 mm, respectively; radioactivity ratio of the background [BG] to outer sphere layer was 1:4; and BG-to-inner sphere layer ratios were 1:1, 1:2, and 1:3) was evaluated. The acquisition time was set at 120 seconds, and imaging was repeated five times. The image data in photomultiplier tube (PMT)-PET were reconstructed using a time-of-flight (TOF) ordered subset expectation maximization (OSEM) algorithm (point spread function [PSF] − , iteration: 3, subset: 10) with a 4-mm Gaussian filter (GF) for normal images. Silicon photomultiplier (SiPM)-PET data were reconstructed using a TOF OSEM algorithm (PSF − , iteration: 2, subset: 12) and a 3-mm GF for normal images. The target images were reconstructed using three CaLM parameters (mild, standard, and strong). All the obtained images were investigated quantitatively, with calculation of maximum standard uptake value (SUVmax), coefficient of variation (CV), and contrast-to-noise ratio (CNR), after setting regions of interest on the lesions. Statistical analysis using the Dunnett's test compared normal images (control group) and target images (treatment group). Statistical significance was considered at p < 0.05. Results Quantitative assessment revealed that the SUVmax of target images (standard and strong) was equivalent to that of normal images in PMT-PET, with SUVmax of 3 to 3.5 for both layers. The SUVmax in SiPM-PET was similar across all CaLM types, ranging from 3 to 4 for all spheres. The target images (standard and strong) had a significantly reduced CV and improved CNR compared with normal images. Conclusion The boundary of the 22/37-mm spheres was visible with CaLM (strong) at radioactivity ratios of 1:4:1 and 1:4:2 on both scanners. For the 13/22-mm sphere boundary, visibility with CaLM (strong) was observed only with SiPM-PET, with the SUVmax equivalent to normal images. CaLM (strong) was deemed the optimal postprocessing filter for PMT-PET due to significant improvements in CV and CNR, while CaLM (standard) was suggested as the optimal filter for SiPM-PET due to excessive BG smoothing.

Adaptive Random Weighted H∞ Estimation for System Noise Statistics

ABSTRACTThe Kalman filter is an important technique for system state estimation. It requires the exact knowledge of system noise statistics to achieve optimal state estimation. However, in practice, this knowledge is often unknown or inaccurate due to uncertainties and disturbances involved in the dynamic environment, leading to degraded or even divergent Kalman filtering solutions. This paper proposes a novel method of H∞ filtering‐based on adaptive random weighted estimation to address this issue. It combines the H∞ filter with random weighted concept to estimate system noise statistics. Random weighting theories are established based on the state estimate and state error covariance of the H∞ filter to estimate both process noise statistics and measurement noise statistics. Subsequently, the estimated system noise statistics are fed back into the Kalman filtering process for system state estimation. Simulation and experimental results show that the proposed method can effectively estimate system noise statistics, leading to improved accuracy for system state estimation.

Adaptive range gating based on variational Bayesian inference for space debris ranging with spaceborne single-photon LiDAR.

To enhance the accuracy of space debris localization, spaceborne single-photon LiDAR (SSPL) presents a promising technique for accurate target ranging. Extended Kalman filtering (EKF) plays a crucial role in range gating under high dynamic and nonlinear motion conditions of space debris, ensuring accurate state estimation and prior distance data. However, unknown and time-varying statistics of process and measurement noise significantly degrade state estimation accuracy, posing risks of filter divergence and reduced photon reception, ultimately rendering range gating ineffective. To address this challenge, we propose an adaptive range gating method based on variational Bayesian adaptive extended Kalman filtering (ARG-VBAEKF). This method leverages variational Bayesian (VB) posterior approximation to estimate the joint distribution of state and noise. Simulation results demonstrate that ARG-VBAEKF achieves accurate state and noise estimation, thereby effectively enhancing range gating performance in SSPL-based space debris ranging.

Simulation study on magneto-acoustic concentration tomography of magnetic nanoparticles based on vectorial acoustic source and BICGSTAB method

Abstract To overcome the vulnerability to noise of the reconstructed image and simplify the cumbersome iteration process of algorithm in the magneto-acoustic concentration tomography with magnetic induction (MACT-MI) for magnetic nanoparticles (MNPs), we established the matrix relationship between the concentration of MNPs and the first-order derivative of sound pressure based on the reconstruction method of vectorial acoustic source, and proposed the application of BICGSTAB method in solving the concentration distribution. Firstly, a simulation model was established in COMSOL Multiphysics. Secondly, the obtained data were substituted into the derived formula for imaging reconstruction. Finally, the quality of the reconstructed image was analyzed. The effects of MNP radius, shape, asymptotic concentration, and SNR on the reconstruction results were studied. Simulation results show that under the same noise condition, compared with the reconstruction method based on the LSQR-trapezoidal method, the average correlation coefficient increased by 32.9%, the average relative error decreased by 48.5%, the average structural similarity increased by 48.2%, and the average iterations decreased by 58.5%. The proposed method shows superior imaging quality and noise immunity. The research provides a theoretical basis for subsequent experimental research.

An alternating minimization algorithm with trajectory for direct exoplanet detection. The AMAT algorithm

Effective image post-processing algorithms are vital for the successful direct imaging of exoplanets. Standard point spread function (PSF) subtraction methods use techniques based on a low-rank approximation to separate the rotating planet signal from the quasi-static speckles and rely on signal-to-noise ratio maps to detect the planet. These steps do not interact or feed each other, leading to potential limitations in the accuracy and efficiency of exoplanet detection. We aim to develop a novel approach that iteratively finds the flux of the planet and the low-rank approximation of quasi-static signals in an attempt to improve upon current PSF subtraction techniques. In this study, we extend the standard L2 norm minimization paradigm to an L1 norm minimization framework in order to better account for noise statistics in the high contrast images. Then, we propose a new method, referred to as the alternating minimization algorithm with trajectory (AMAT), that makes more advanced use of estimating the low-rank approximation of the speckle field and the planet flux by alternating between them and utilizing both L1 and L2 norms. For the L1 norm minimization, we propose using L1 norm low-rank approximation (L1-LRA), a low-rank approximation computed using an exact block-cyclic coordinate descent method, while we use randomized singular value decomposition for the L2 norm minimization. Additionally, we enhance the visibility of the planet signal using a likelihood ratio as a post-processing step. Numerical experiments performed on a VLT/SPHERE-IRDIS dataset show the potential of AMAT to improve upon the existing approaches in terms of higher S/N, sensitivity limits (contrast curves), and receiver operating characteristic curves. Moreover, for a systematic comparison, we used datasets from the exoplanet data challenge to compare our algorithm with other algorithms in the challenge, and we find AMAT with a likelihood ratio map performs better than most algorithms tested on the exoplanet data challenge.

Film image processing and production based on high-performance calculation

In film and television production, efficient and precise image processing is vital for achieving realistic visual effects. Therefore, exploring and applying advanced image processing technologies has become an essential method for elevating the production quality of film and television projects. This work investigates the application of artificial intelligence (AI) technology in the processing and production of animated images in film and television scenarios. By comparing the performance of standard Generative Adversarial Network (GAN), DenseNet, and CycleGAN models under different noise conditions, it is found that CycleGAN performs the best in image denoising and detail restoration. Experimental results demonstrate that CycleGAN achieves a Peak Signal-to-noise Ratio (PSNR) of 30.1dB and a Structural Similarity Index Measure (SSIM) of 0.88 under Gaussian noise conditions. Moreover, CycleGAN achieves a PSNR of 29.5dB and an SSIM of 0.85 under salt-and-pepper noise conditions. It outperforms the other models in both conditions. Additionally, CycleGAN’s mean absolute error is significantly lower than that of the other models. This work demonstrates that CycleGAN can more effectively handle complex noise and generate high-quality images under unsupervised learning conditions. These findings provide new directions for future image processing research and offer important references for model selection in practical applications. This work not only offers new perspectives on the development of animation image processing technology but also establishes a theoretical foundation for applying advanced AI techniques in film and television production. Through comparative analysis of various deep learning models, this work highlights the superior performance of CycleGAN under complex noise conditions. This advancement not only drives progress in image processing technology but also provides effective solutions for efficient production and quality enhancement of future film and television works.

A novel bearing weak fault diagnosis method based on rank constrained low-rank and sparse decomposition

Abstract Addressing the challenge of diagnosing incipient bearing faults amidst significant noise, a novel diagnostic approach is introduced, leveraging a Rank Constrained Low-Rank and Sparse Decomposition (RCLRSD) model tailored for weak fault detection in bearings. Initially, we raised the Autocorrelation Function of the Square Envelope in Frequency Domain (AFSEFD) as an innovative method for the estimation of fault frequencies. Subsequently, we constructed a two-dimensional observation matrix, which is formulated independently of predefined assumptions. Then, we examine the configuration and distribution patterns of bearing fault signals, uncovering the low-rank nature of fault characteristics within a designated two-dimensional transform domain. Moreover, we found the noise signal to exhibit sparsity and an approximate Gaussian distribution. Based on this, a rank-constrained low-rank sparse decomposition model is established, and rank-constrained low-rank regular constraints for feature information and sparse regular constraints and Gaussian constraints for interference signals are constructed respectively. Ultimately, we employed the Gray Wolf Optimization (GWO) algorithm to refine the model parameters, and we deduced the model's solver via the Alternating Direction Method of Multipliers (ADMM). The proposed RCLRSD model decomposes bearing fault data into three constituents: low-rank, sparse, and Gaussian components, effectively addressing the challenge of extracting weak fault signatures from bearings. The weak feature extraction capability of the RCLRSD model is verified using a multi-interference simulation model and experimental data of bearing failures under strong noise conditions; the generalization of the model is verified by the classification effect of the Support Vector Machine (SVM) under two bearing failure datasets. Comparison with various algorithms confirms the superiority of the proposed algorithm.

Adaptive Multi-Scale Bayesian Framework for MFL Inspection of Steel Wire Ropes

Magnetic flux leakage (MFL) technology is widely used in steel wire rope (SWR) inspection for non-destructive testing. However, accurate defect characterization requires advanced signal processing techniques to handle complex noise conditions and varying defect types. This paper presents a novel adaptive multi-scale Bayesian framework for MFL signal analysis in SWR inspection. Our approach integrates discrete wavelet transform with adaptive thresholding and multi-scale feature fusion, enabling simultaneous detection of minute defects and large-area corrosion. To validate our method, we implemented a four-channel MFL detection system and conducted extensive experiments on both simulated and real-world datasets. Compared with state-of-the-art methods, including long short-term memory (LSTM), attention mechanisms, and isolation forests, our approach demonstrated significant improvements in precision, recall, and F1 score across various tolerance levels. The proposed method showed superior detection performance, with an average precision of 91%, recall of 89%, and an F1 score of 0.90 in high-noise conditions, surpassing existing techniques. Notably, our method showed superior performance in high-noise environments, reducing false positive rates while maintaining high detection sensitivity. While computational complexity in real-time processing remains a challenge, this study provides a robust solution for non-destructive testing of SWR, potentially improving inspection efficiency and defect localization accuracy. Future work will focus on optimizing algorithmic efficiency and exploring transfer learning techniques for enhanced adaptability across different non-destructive testing (NDT) domains. This research not only advances signal processing and anomaly detection technology but also contributes to enhancing safety and maintenance efficiency in critical infrastructure.

Prediction intervals with controlled length in the heteroscedastic Gaussian regression

We tackle the problem of building a prediction interval in heteroscedastic Gaussian regression. We focus on prediction intervals with constrained expected length in order to guarantee interpretability of the output. In this framework, we derive a closed-form expression of the optimal prediction interval that allows for the development of a data-driven prediction interval based on plug-in. The construction of the proposed algorithm is based on two samples, one labelled and another unlabelled. Under mild conditions, we show that our procedure is asymptotically as good as the optimal prediction interval both in terms of expected length and error rate. In particular, the control of the expected length is distribution-free. We also derive rates of convergence under smoothness and the Tsybakov noise conditions. We conduct a numerical analysis that exhibits the good performance of our method. It also indicates that even with a few amount of unlabelled data, our method is very effective in enforcing the length constraint.

A new QRS detector stress test combining temporal jitter and F-score (JF) reveals significant performance differences amongst popular detectors.

QRS detection within an electrocardiogram (ECG) is the basis of virtually any further processing and any error caused by this detection will propagate to further processing stages. However, standard benchmarking procedures of QRS detectors are seriously flawed because they report almost always close to 100% accuracy for any QRS detection algorithm. This is due to the use of large temporal error margins and noise-free ECG databases which grossly overestimate their performance. The use of a large fixed error margin masks temporal jitter between detection and ground truth measurements. Here, we present a new performance measure (JF) which combines temporal jitter with the F-score, and also an ECG database with decreasing levels of signal to noise ratios based on noise generated from different tasks. Our new performance measure JF fully encompasses all the types of errors that can occur, equally weights them and provides a percentage value which allows direct comparison between QRS detection algorithms. In combination with the new noisy ECG database, the JF performance measure now varies between 50% and 100% for different detectors and signal to noise conditions thereby making it possible to find the best detector for an application.

Attribute Relevance Score: A Novel Measure for Identifying Attribute Importance

This study introduces a novel measure for evaluating attribute relevance, specifically designed to accurately identify attributes that are intrinsically related to a phenomenon, while being sensitive to the asymmetry of those relationships and noise conditions. Traditional variable selection techniques, such as filter and wrapper methods, often fall short in capturing these complexities. Our methodology, grounded in decision trees but extendable to other machine learning models, was rigorously evaluated across various data scenarios. The results demonstrate that our measure effectively distinguishes relevant from irrelevant attributes and highlights how relevance is influenced by noise, providing a more nuanced understanding compared to established methods such as Pearson, Spearman, Kendall, MIC, MAS, MEV, GMIC, and Phik. This research underscores the importance of phenomenon-centric explainability, reproducibility, and robust attribute relevance evaluation in the development of predictive models. By enhancing both the interpretability and contextual accuracy of models, our approach not only supports more informed decision making but also contributes to a deeper understanding of the underlying mechanisms in diverse application domains, such as biomedical research, financial modeling, astronomy, and others.

Robust Biometric Verification Using Phonocardiogram Fingerprinting and a Multilayer-Perceptron-Based Classifier

Recently, a new set of biometric traits, called medical biometrics, have been explored for human identity verification. This study introduces a novel framework for recognizing human identity through heart sound signals, commonly referred to as phonocardiograms (PCGs). The framework is built on extracting and suitably processing Mel-Frequency Cepstral Coefficients (MFCCs) from PCGs and on a classifier based on a Multilayer Perceptron (MLP) network. A large dataset containing heart sounds acquired from 206 people has been used to perform the experiments. The classifier was tuned to obtain the same false positive and false negative misclassification rates (equal error rate: EER = FPR = FNR) on chunks of audio lasting 2 s. This target has been reached, splitting the dataset into 70% and 30% training and testing non-overlapped subsets, respectively. A recurrence filter has been applied to also improve the performance of the system in the presence of noisy recordings. After the application of the filter on chunks of audio signal lasting from 2 to 22 s, the performance of the system has been evaluated in terms of recall, specificity, precision, negative predictive value, accuracy, and F1-score. All the performance metrics are higher than 97.86% with the recurrence filter applied on a window lasting 22 s and in different noise conditions.

Impact of Adverse Weather and Image Distortions on Vision-Based UAV Detection: A Performance Evaluation of Deep Learning Models

Unmanned aerial vehicle (UAV) detection in real-time is a challenging task despite the advances in computer vision and deep learning techniques. The increasing use of UAVs in numerous applications has generated worries about possible risks and misuse. Although vision-based UAV detection methods have been proposed in recent years, a standing open challenge and overlooked issue is that of adverse weather. This work is the first, to the best of our knowledge, to investigate the impact of adverse weather conditions and image distortions on vision-based UAV detection methods. To achieve this, a custom training dataset was curated with images containing a variety of UAVs in diverse complex backgrounds. In addition, this work develops a first-of-its-kind dataset, to the best of our knowledge, with UAV-containing images affected by adverse conditions. Based on the proposed datasets, a comprehensive benchmarking study is conducted to evaluate the impact of adverse weather and image distortions on the performance of popular object detection methods such as YOLOv5, YOLOv8, Faster-RCNN, RetinaNet, and YOLO-NAS. The experimental results reveal the weaknesses of the studied models and the performance degradation due to adverse weather, highlighting avenues for future improvement. The results show that even the best UAV detection model’s performance degrades in mean average precision (mAP) by −50.62 points in torrential rain conditions, by −52.40 points in high noise conditions, and by −77.0 points in high motion blur conditions. To increase the selected models’ resilience, we propose and evaluate a strategy to enhance the training of the selected models by introducing weather effects in the training images. For example, the YOLOv5 model with the proposed enhancement strategy gained +35.4, +39.3, and +44.9 points higher mAP in severe rain, noise, and motion blur conditions respectively. The findings presented in this work highlight the advantages of considering adverse weather conditions during model training and underscore the significance of data enrichment for improving model generalization. The work also accentuates the need for further research into advanced techniques and architectures to ensure more reliable UAV detection under extreme weather conditions and image distortions.

Low-dose radiographic inspection of welding by a novel aperiodic reverse stochastic resonance method

Abstract Low-dose radiographic inspection is a growing trend in industry to minimize radiation risks to humans and the environment. However, reduction in radiation dose often introduces significant noise, which affects image quality and hinders accurate identification of subtle defects. This study addresses this issue by introducing a novel phenomenon called aperiodic reverse stochastic resonance (ARSR), observed in nonlinear systems excited by aperiodic binary signals. ARSR enables simultaneous amplitude amplification and reversal of signals under specific noise conditions. Leveraging ARSR, we propose an image denoising framework for low-dose radiographic inspections. First, a set of projection data is obtained by using Radon transform to reduce the dimensionality of x-ray images from different angles. Then, the projection data is modulated based on the ARSR system. Finally, the image is reconstructed based on the inverse Radon transform. Simulations and experimental comparison results in welding applications validate the effectiveness of the framework, demonstrating significant improvements in image quality for low-dose radiographic defect detection. Unlike advanced methods such as Gaussian filtering, BM3D, and DnCNN, which operate at the pixel level, ARSR performs denoising at the projection data stage, reducing noise impact, preserving original information, and focusing on physical data processing during imaging. This approach enhances the detection of subtle defects, highlighting the potential of stochastic resonance in image processing.

Improved analytical solution with optimization constraints using TDOA and FDOA measurements for USV/AUV collaborative localization

The paper introduces an enhanced constrained two-step weighted least squares (WLS) analytic localization algorithm designed to determine the AUV’s position and velocity within the collaborative localization system, utilizing time difference of arrival and frequency difference of arrival measurements. This algorithm integrates optimization constraints between intermediate variables and target motion parameters, producing precise analytical solution based on WLS minimization criterion. The proposed process not only reduces computational burden by providing an analytical solution but also enhances estimation accuracy through the incorporation of optimization constraints. Analytical assessments and statistical simulations highlight the superior estimation accuracy of the proposed algorithm, and demonstrate that the position and velocity estimation accuracy align with the Cramér-Rao lower bound under appropriate measurement noise conditions.

Reducing statistical noise in frequency ratio measurement between Ca+ and Sr optical clocks with a frequency-synthesized local oscillator from a Sr optical clock

Optical frequency ratio measurement between optical atomic clocks is essential to precision measurement as well as the redefinition of the second. Currently, the statistical noise in frequency ratio measurement of most ion clocks is limited by the frequency instability of ion clocks. In this work, we reduce the statistical noise in the frequency ratio measurement between a transportable Ca+ optical clock and a Sr optical lattice clock down to 2.2×10−15/τ. The local oscillator of the Ca+ optical clock is frequency-synthesized from the Sr optical lattice clock, enabling a longer probe time for Ca+ clock transition. Compared to previous measurement using independent local oscillators, we achieve 10-fold reduction in comparison campaign duration.

Differential Analysis of Emergency Vehicle Detection in Urban Traffic : A Systematic Review

The differential analysis of emergency vehicle detection in urban traffic is crucial for improving response times and reducing traffic-related delays during emergencies. This systematic review aims to analyze various methods and technologies, such as acoustic, visual, and sensor-based systems, used for detecting emergency vehicles in complex urban environments. The motivation behind this study is the growing need for more efficient traffic management systems that prioritize emergency vehicles, minimizing delays caused by congestion. However, limitations include the inconsistent performance of detection systems in varying weather, lighting, and noise conditions, as well as integration challenges with existing infrastructure. The objective is to evaluate current detection methods, identify their limitations, and propose potential improvements to enhance the accuracy and reliability of emergency vehicle detection in urban traffic systems.

Granger Causal Inference Based on Dual Laplacian Distribution and Its Application to MI-BCI Classification.

Granger causality-based effective brain connectivity provides a powerful tool to probe the neural mechanism for information processing and the potential features for brain computer interfaces. However, in real applications, traditional Granger causality is prone to the influence of outliers, such as inevitable ocular artifacts, resulting in unreasonable brain linkages and the failure to decipher inherent cognition states. In this work, motivated by constructing the sparse causality brain networks under the strong physiological outlier noise conditions, we proposed a dual Laplacian Granger causality analysis (DLap-GCA) by imposing Laplacian distributions on both model parameters and residuals. In essence, the first Laplacian assumption on residuals will resist the influence of outliers in electroencephalogram (EEG) on causality inference, and the second Laplacian assumption on model parameters will sparsely characterize the intrinsic interactions among multiple brain regions. Through simulation study, we quantitatively verified its effectiveness in suppressing the influence of complex outliers, the stable capacity for model estimation, and sparse network inference. The application to motor-imagery (MI) EEG further reveals that our method can effectively capture the inherent hemispheric lateralization of MI tasks with sparse patterns even under strong noise conditions. The MI classification based on the network features derived from the proposed approach shows higher accuracy than other existing traditional approaches, which is attributed to the discriminative network structures being captured in a timely manner by DLap-GCA even under the single-trial online condition. Basically, these results consistently show its robustness to the influence of complex outliers and the capability of characterizing representative brain networks for cognition information processing, which has the potential to offer reliable network structures for both cognitive studies and future brain-computer interface (BCI) realization.

Multitask-Transfer-Learning Method for Random-Force Frequency Identification Considering Multisource Uncertainties

Accurate reconstruction of unknown external forces from measurable responses is critical for ensuring structural safety and minimizing maintenance costs of aircraft structures. This paper presents a novel multitask-transfer-learning method for random-force frequency identification that accounts for modeling and measurement uncertainties. A data-driven convolutional neural network (CNN) model is utilized to capture the relationship between the power spectral densities of external forces and measured responses, addressing the inherent ill-posedness of traditional model-driven force identification methods. To shorten the frequency-dependent training time in the full frequency domain, a transfer-learning strategy is implemented, fine-tuning hyperparameters from a CNN model trained at one source frequency to another target frequency. Furthermore, an iterative dimensionwise collocation method based on nonprobabilistic interval modeling is introduced to quantify the uncertain boundaries of external loads caused by multisource uncertainties. By incorporating a multitask-learning framework, the process of establishing CNN models for collocated samples is accelerated, reducing the computational effort for uncertainty quantification. The proposed method is validated through both numerical and experimental examples, demonstrating its accuracy, robustness, and computational efficiency for force identification in the full frequency domain, even under conditions of insufficient measurements, measurement noises, and material dispersions.

Performance comparison of the Shack-Hartmann and pyramid wavefront sensors with a laser guide star for 40 m telescopes

Context. Upcoming giant segmented mirror telescopes will use laser guide stars (LGS) for their adaptive optics (AO) systems. Two options of wavefront sensors (WFSs) are the Shack-Hartmann wavefront sensor (SHWFS) and the pyramid wavefront sensor (PWFS). Aims. In this paper, we compare the noise performance of the PWFS and the SHWFS. We aim to identify which of the two is best to use in the context of a single or tomographic configuration. Methods. To compute the noise performance, we extended a noise model developed for the PWFS to be used with the SHWFS. To do this, we expressed the centroiding algorithm of the SHWFS as a matrix-vector multiplication, which allowed us to use the statistics of noise to compute its propagation through the AO loop. We validated the noise model with end-to-end simulations for telescopes of 8 and 16 m in diameter. Results. For an AO system with only one WFS, we found that given the same number of subapertures, the PWFS outperforms the SHWFS. For a 40 m telescope, the limiting magnitude of the PWFS is around one magnitude higher than the SHWFS. When using multiple WFS and a generalized least-squares estimator to combine the signal, our model predicts that in a tomographic system, the SHWFS performs better than the PWFS (with a limiting magnitude that is higher by a 0.3 magnitude. When using sub-electron RON detectors for the PWFS, the performance quality is almost identical for the two WFSs. Conclusions. We find that when using a single WFS with LGS, PWFS is a better alternative than the SH. For a tomographic system, both sensors would give roughly the same performance.