660 research outputs found

    Data augmentation for galaxy density map reconstruction

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    The matter density is an important knowledge for today cosmology as many phenomena are linked to matter fluctuations. However, this density is not directly available, but estimated through lensing maps or galaxy surveys. In this article, we focus on galaxy surveys which are incomplete and noisy observations of the galaxy density. Incomplete, as part of the sky is unobserved or unreliable. Noisy as they are count maps degraded by Poisson noise. Using a data augmentation method, we propose a two-step method for recovering the density map, one step for inferring missing data and one for estimating of the density. The results show that the missing areas are efficiently inferred and the statistical properties of the maps are very well preserved

    A Few Photons Among Many: Unmixing Signal and Noise for Photon-Efficient Active Imaging

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    Conventional LIDAR systems require hundreds or thousands of photon detections to form accurate depth and reflectivity images. Recent photon-efficient computational imaging methods are remarkably effective with only 1.0 to 3.0 detected photons per pixel, but they are not demonstrated at signal-to-background ratio (SBR) below 1.0 because their imaging accuracies degrade significantly in the presence of high background noise. We introduce a new approach to depth and reflectivity estimation that focuses on unmixing contributions from signal and noise sources. At each pixel in an image, short-duration range gates are adaptively determined and applied to remove detections likely to be due to noise. For pixels with too few detections to perform this censoring accurately, we borrow data from neighboring pixels to improve depth estimates, where the neighborhood formation is also adaptive to scene content. Algorithm performance is demonstrated on experimental data at varying levels of noise. Results show improved performance of both reflectivity and depth estimates over state-of-the-art methods, especially at low signal-to-background ratios. In particular, accurate imaging is demonstrated with SBR as low as 0.04. This validation of a photon-efficient, noise-tolerant method demonstrates the viability of rapid, long-range, and low-power LIDAR imaging

    A hybrid approach to CMB lensing reconstruction on all-sky intensity maps

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    Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous noise. For l < 100, we show that a full-sky inpainting method, already described in a previous work, still allows a minimal variance reconstruction, with a bias that must be accounted for by a Monte-Carlo method, but that does not couple to the deflection field. For l>100 we develop a method based on tiling the cut-sky with local 10x10 degrees overlapping tangent planes (referred to in the following as "patches"). It requires to solve various issues concerning their size/position, non-periodic boundaries and irregularly sampled data after the sphere-to-plane projection. We show how the leading noise term of the quadratic lensing estimator applied onto an apodized patch can still be taken directly from the data. To not loose spatial accuracy, we developed a tool that allows the fast determination of the complex Fourier series coefficients from a bi-dimensional irregularly sampled dataset, without performing an interpolation. We show that the multi-patch approach allows the lensing power spectrum reconstruction with a very small bias, thanks to avoiding the galactic mask and lowering the noise inhomogeneities, while still having almost a minimal variance. The data quality can be assessed at each stage and simple bi-dimensional spectra build, which allows the control of local systematic errors.Comment: A&A version. Mostly english correction

    Monte Carlo guided Diffusion for Bayesian linear inverse problems

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    Ill-posed linear inverse problems that combine knowledge of the forward measurement model with prior models arise frequently in various applications, from computational photography to medical imaging. Recent research has focused on solving these problems with score-based generative models (SGMs) that produce perceptually plausible images, especially in inpainting problems. In this study, we exploit the particular structure of the prior defined in the SGM to formulate recovery in a Bayesian framework as a Feynman--Kac model adapted from the forward diffusion model used to construct score-based diffusion. To solve this Feynman--Kac problem, we propose the use of Sequential Monte Carlo methods. The proposed algorithm, MCGdiff, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems.Comment: preprin

    Image processing techniques for high-speed atomic force microscopy

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    Atomic force microscopy (AFM) is a powerful tool for imaging topography or other characteristics of sample surfaces at nanometer-scale spatial resolution by recording the interaction of a sharp probe with the surface. Dispute its excellent spatial resolution, one of the enduring challenges in AFM imaging is its poor temporal resolution relative to the rate of dynamics in many systems of interest. This has led to a large research effort on the development of high-speed AFM (HS-AFM). Most of these efforts focus on mechanical improvement and control algorithm design. This dissertation investigates a complementary HS-AFM approach based on the idea of undersampling which aims at increasing the imaging rate of the instrument by reducing the number of pixels in the sample surface that need to be acquired to create a high-quality image. The first part of this work focuses on the reconstruction of images sub-sampled according to a scheme known as μ path patterns. These patterns consist of randomly placed short and disjoint scans and are designed specifically for fast, efficient, and consistent data acquisition in AFM. We compare compressive sensing (CS) reconstruction methods with inpainting methods on recovering μ-path undersampled images. The results illustrate that the reconstruction quality depends on the choice of reconstruction methods and the sample under study, with CS generally producing a superior result for samples with sparse frequency content and inpainting performing better for samples with information limited to low frequencies. Motivated by the comparison, a basis pursuit vertical variation (BPVV) method, combing CS and inpainting, is proposed. Based on single image reconstruction results, we also extend our analysis to the problem of multiple AFM frames, in which higher overall video reconstruction quality is achieved by pixel sharing among different frames. The second part of the thesis considers patterns for sub-sampling in AFM. The allocation of measurements plays an important role in producing accurate reconstructions of the sample surface. We analyze the expected image reconstruction error using a greedy CS algorithm of our design, termed simplified matching pursuit (SMP), and propose a Monte Carlo-based strategy to create μ-path patterns that minimize the expected error. Because these μ path patterns involve a collection of disjoint scan paths, they require the tip of the instrument to be repeatedly lifted from and re-engaged to the surface. In many cases, the re-engagements make up a significant portion of the total data acquisition time. We therefore extend our Monte Carlo design strategy to find continuous scan patterns that minimize the reconstruction error without requiring the tip to be lifted from the surface. For the final part of the work, we provide a hardware demonstration on a commercial AFM. We describe hardware implementation details and image a calibration grating using the proposed μ-path and continuous scan patterns. The sample surface is reconstructed from acquired data using CS and inpainting methods. The recovered image quality and achievable imaging rate are compared to full raster-scans of the sample. The experimental results show that the proposed scanning combining with reconstruction methods can produce higher image quality with less imaging time

    Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems

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    In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multi-scale problems. BPINNs are a popular framework for data assimilation, combining the constraints of Uncertainty Quantification (UQ) and Partial Differential Equation (PDE). The relative weights of the BPINN target distribution terms are directly related to the inherent uncertainty in the respective learning tasks. Yet, they are usually manually set a-priori, that can lead to pathological behavior, stability concerns, and to conflicts between tasks which are obstacles that have deterred the use of BPINNs for inverse problems with multi-scale dynamics. The present weighting strategy automatically tunes the weights by considering the multi-task nature of target posterior distribution. We show that this remedies the failure modes of BPINNs and provides efficient exploration of the optimal Pareto front. This leads to better convergence and stability of BPINN training while reducing sampling bias. The determined weights moreover carry information about task uncertainties, reflecting noise levels in the data and adequacy of the PDE model. We demonstrate this in numerical experiments in Sobolev training, and compare them to analytically ϵ\epsilon-optimal baseline, and in a multi-scale Lokta-Volterra inverse problem. We eventually apply this framework to an inpainting task and an inverse problem, involving latent field recovery for incompressible flow in complex geometries
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