A multiscale regularized restoration algorithm for XMM-Newton data

We introduce a new multiscale restoration algorithm for images with few photons counts and its use for denoising XMM data. We use a thresholding of the wavelet space so as to remove the noise contribution at each scale while preserving the multiscale information of the signal. Contrary to other algorithms the signal restoration process is the same whatever the signal to noise ratio is. Thresholds according to a Poisson noise process are indeed computed analytically at each scale thanks to the use of the unnormalized Haar wavelet transform. Promising preliminary results are obtained on X-ray data for Abell 2163 with the computation of a temperature map.Comment: To appear in the Proceedings of `Galaxy Clusters and the High Redshift Universe Observed in X-rays', XXIth Moriond Astrophysics Meeting (March 2001), Eds. Doris Neumann et a

On the effect of image denoising on galaxy shape measurements

Weak gravitational lensing is a very sensitive way of measuring cosmological parameters, including dark energy, and of testing current theories of gravitation. In practice, this requires exquisite measurement of the shapes of billions of galaxies over large areas of the sky, as may be obtained with the EUCLID and WFIRST satellites. For a given survey depth, applying image denoising to the data both improves the accuracy of the shape measurements and increases the number density of galaxies with a measurable shape. We perform simple tests of three different denoising techniques, using synthetic data. We propose a new and simple denoising method, based on wavelet decomposition of the data and a Wiener filtering of the resulting wavelet coefficients. When applied to the GREAT08 challenge dataset, this technique allows us to improve the quality factor of the measurement (Q; GREAT08 definition), by up to a factor of two. We demonstrate that the typical pixel size of the EUCLID optical channel will allow us to use image denoising.Comment: Accepted for publication in A&A. 8 pages, 5 figure

Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows

This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This includes Riemannian gradient flow systems which occur naturally in optimization problems. The Itoh--Abe discrete gradient is formulated and applied to gradient systems, yielding a derivative-free optimization algorithm. The algorithm is tested on two eigenvalue problems and two problems from manifold valued imaging: InSAR denoising and DTI denoising.Comment: Post-revision version. To appear in SIAM Journal on Scientific Computin

PERSIANN-CNN: Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks-Convolutional Neural Networks

Abstract Accurate and timely precipitation estimates are critical for monitoring and forecasting natural disasters such as floods. Despite having high-resolution satellite information, precipitation estimation from remotely sensed data still suffers from methodological limitations. State-of-the-art deep learning algorithms, renowned for their skill in learning accurate patterns within large and complex datasets, appear well suited to the task of precipitation estimation, given the ample amount of high-resolution satellite data. In this study, the effectiveness of applying convolutional neural networks (CNNs) together with the infrared (IR) and water vapor (WV) channels from geostationary satellites for estimating precipitation rate is explored. The proposed model performances are evaluated during summer 2012 and 2013 over central CONUS at the spatial resolution of 0.08° and at an hourly time scale. Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN)–Cloud Classification System (CCS), which is an operational satellite-based product, and PERSIANN–Stacked Denoising Autoencoder (PERSIANN-SDAE) are employed as baseline models. Results demonstrate that the proposed model (PERSIANN-CNN) provides more accurate rainfall estimates compared to the baseline models at various temporal and spatial scales. Specifically, PERSIANN-CNN outperforms PERSIANN-CCS (and PERSIANN-SDAE) by 54% (and 23%) in the critical success index (CSI), demonstrating the detection skills of the model. Furthermore, the root-mean-square error (RMSE) of the rainfall estimates with respect to the National Centers for Environmental Prediction (NCEP) Stage IV gauge–radar data, for PERSIANN-CNN was lower than that of PERSIANN-CCS (PERSIANN-SDAE) by 37% (14%), showing the estimation accuracy of the proposed model

On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs

Soft wavelet shrinkage, total variation (TV) diffusion, total variation regularization, and a dynamical system called SIDEs are four useful techniques for discontinuity preserving denoising of signals and images. In this paper we investigate under which circumstances these methods are equivalent in the 1-D case. First we prove that Haar wavelet shrinkage on a single scale is equivalent to a single step of space-discrete TV diffusion or regularization of two-pixel pairs. In the translationally invariant case we show that applying cycle spinning to Haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of TV diffusion. We prove that space-discrete TV difusion and TV regularization are identical, and that they are also equivalent to the SIDEs system when a specific force function is chosen. Afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the Laplacian pyramid of the signal. We analyse possibilities to avoid Gibbs-like artifacts for multiscale Haar wavelet shrinkage by scaling the thesholds. Finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and PDE / variational approaches. These methods are based on iterated shift-invariant wavelet shrinkage at multiple scales with scaled thresholds