Measurement and Calibration of Noise Bias in Weak Lensing Galaxy Shape Estimation

Weak gravitational lensing has the potential to constrain cosmological parameters to high precision. However, as shown by the Shear TEsting Programmes (STEP) and GRavitational lEnsing Accuracy Testing (GREAT) Challenges, measuring galaxy shears is a nontrivial task: various methods introduce different systematic biases which have to be accounted for. We investigate how pixel noise on the image affects the bias on shear estimates from a Maximum-Likelihood forward model-fitting approach using a sum of co-elliptical S\'{e}rsic profiles, in complement to the theoretical approach of an an associated paper. We evaluate the bias using a simple but realistic galaxy model and find that the effects of noise alone can cause biases of order 1-10% on measured shears, which is significant for current and future lensing surveys. We evaluate a simulation-based calibration method to create a bias model as a function of galaxy properties and observing conditions. This model is then used to correct the simulated measurements. We demonstrate that this method can effectively reduce noise bias so that shear measurement reaches the level of accuracy required for estimating cosmic shear in upcoming lensing surveys.Comment: 12 pages, 4 figures, submitted to MNRA

S\'{e}rsic galaxy models in weak lensing shape measurement: model bias, noise bias and their interaction

Cosmic shear is a powerful probe of cosmological parameters, but its potential can be fully utilised only if galaxy shapes are measured with great accuracy. Two major effects have been identified which are likely to account for most of the bias for maximum likelihood methods in recent shear measurement challenges. Model bias occurs when the true galaxy shape is not well represented by the fitted model. Noise bias occurs due to the non-linear relationship between image pixels and galaxy shape. In this paper we investigate the potential interplay between these two effects when an imperfect model is used in the presence of high noise. We present analytical expressions for this bias, which depends on the residual difference between the model and real data. They can lead to biases not accounted for in previous calibration schemes. By measuring the model bias, noise bias and their interaction, we provide a complete statistical framework for measuring galaxy shapes with model fitting methods from GRavitational lEnsing Accuracy Testing (GREAT) like images. We demonstrate the noise and model interaction bias using a simple toy model, which indicates that this effect can potentially be significant. Using real galaxy images from the Cosmological Evolution Survey (COSMOS) we quantify the strength of the model bias, noise bias and their interaction. We find that the interaction term is often a similar size to the model bias term, and is smaller than the requirements of the current and shortly upcoming galaxy surveys.Comment: 11 pages, 3 figure

Noise Suppression of Computed Tomography (CT) Images Using Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)

In this study, an in-house residual encoder-decoder convolutional neural network (RED-CNN)-based algorithm was composed and trained using images of cylindrical polymethyl-methacrylate (PMMA) phantom with a diameter of 26 cm at different simulated noise levels. The model was tested on 21 × 26 cm elliptical PMMA computed tomography (CT) phantom images with simulated noise to evaluate its denoising capability using signal to noise ratio (SNR), comparative peak signal-to-noise ratio (cPSNR), structural similarity (SSIM) index, modulation transfer function frequencies (MTF 10 %) and noise power spectra (NPS) values as parameters. Evaluation of a possible decrease of image quality was also performed by testing the model using homogenous water phantom and wire phantom images acquired using different mAs values. Results show that the model was able to consistently increase SNR, cPSNR, SSIM values, and decrease the integral noise power spectra (NPS). However, the noise level on either training or testing data affects the model’s final denoising performance. The lower noise level on testing data images tends to result in over-smoothed images, as indicated by the shift of the NPS curves. In contrast, higher simulated noise level tends to result in less satisfactory denoising performance, as indicated by lower SNR, cPSNR, and SSIM values. Meanwhile, the higher noise level on training data images tends to produce denoised images with reduced sharpness, as indicated by the decrease of the MTF 10 % values. Further studies are required to better understand the character of RED-CNN for CT noise suppression regarding the optimum parameters for best results

Multiple Testing and Variable Selection along Least Angle Regression's path

In this article, we investigate multiple testing and variable selection using Least Angle Regression (LARS) algorithm in high dimensions under the Gaussian noise assumption. LARS is known to produce a piecewise affine solutions path with change points referred to as knots of the LARS path. The cornerstone of the present work is the expression in closed form of the exact joint law of K-uplets of knots conditional on the variables selected by LARS, namely the so-called post-selection joint law of the LARS knots. Numerical experiments demonstrate the perfect fit of our finding. Our main contributions are three fold. First, we build testing procedures on variables entering the model along the LARS path in the general design case when the noise level can be unknown. This testing procedures are referred to as the Generalized t-Spacing tests (GtSt) and we prove that they have exact non-asymptotic level (i.e., Type I error is exactly controlled). In that way, we extend a work from (Taylor et al., 2014) where the Spacing test works for consecutive knots and known variance. Second, we introduce a new exact multiple false negatives test after model selection in the general design case when the noise level can be unknown. We prove that this testing procedure has exact non-asymptotic level for general design and unknown noise level. Last, we give an exact control of the false discovery rate (FDR) under orthogonal design assumption. Monte-Carlo simulations and a real data experiment are provided to illustrate our results in this case. Of independent interest, we introduce an equivalent formulation of LARS algorithm based on a recursive function.Comment: 62 pages; new: FDR control and power comparison between Knockoff, FCD, Slope and our proposed method; new: the introduction has been revised and now present a synthetic presentation of the main results. We believe that this introduction brings new insists compared to previous version

Transient excitation and data processing techniques employing the fast fourier transform for aeroelastic testing

The development of testing techniques useful in airplane ground resonance testing, wind tunnel aeroelastic model testing, and airplane flight flutter testing is presented. Included is the consideration of impulsive excitation, steady-state sinusoidal excitation, and random and pseudorandom excitation. Reasons for the selection of fast sine sweeps for transient excitation are given. The use of the fast fourier transform dynamic analyzer (HP-5451B) is presented, together with a curve fitting data process in the Laplace domain to experimentally evaluate values of generalized mass, model frequencies, dampings, and mode shapes. The effects of poor signal to noise ratios due to turbulence creating data variance are discussed. Data manipulation techniques used to overcome variance problems are also included. The experience is described that was gained by using these techniques since the early stages of the SST program. Data measured during 747 flight flutter tests, and SST, YC-14, and 727 empennage flutter model tests are included

Improved method for SNR prediction in machine-learning-based test

This paper applies an improved method for testing the signal-to-noise ratio (SNR) of Analogue-to-Digital Converters (ADC). In previous work, a noisy and nonlinear pulse signal is exploited as the input stimulus to obtain the signature results of ADC. By applying a machine-learning-based approach, the dynamic parameters can be predicted by using the signature results. However, it can only estimate the SNR accurately within a certain range. In order to overcome this limitation, an improved method based on work is applied in this work. It is validated on the Labview model of a 12-bit 80 Ms/s pipelined ADC with a pulse- wave input signal of 3 LSB noise and 7-bit nonlinear rising and falling edges