Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing

Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets or curvelets have also been proposed for the detection of anisotropic features such cosmic strings in the cosmic microwave background. We review in this paper a range of methods based on sparsity that have been proposed for astronomical data analysis. We also discuss what is the impact of Compressed Sensing, the new sampling theory, in astronomy for collecting the data, transferring them to the earth or reconstructing an image from incomplete measurements.Comment: Submitted. Full paper will figures available at http://jstarck.free.fr/IEEE09_SparseAstro.pd

Universal Denoising Networks : A Novel CNN Architecture for Image Denoising

We design a novel network architecture for learning discriminative image models that are employed to efficiently tackle the problem of grayscale and color image denoising. Based on the proposed architecture, we introduce two different variants. The first network involves convolutional layers as a core component, while the second one relies instead on non-local filtering layers and thus it is able to exploit the inherent non-local self-similarity property of natural images. As opposed to most of the existing deep network approaches, which require the training of a specific model for each considered noise level, the proposed models are able to handle a wide range of noise levels using a single set of learned parameters, while they are very robust when the noise degrading the latent image does not match the statistics of the noise used during training. The latter argument is supported by results that we report on publicly available images corrupted by unknown noise and which we compare against solutions obtained by competing methods. At the same time the introduced networks achieve excellent results under additive white Gaussian noise (AWGN), which are comparable to those of the current state-of-the-art network, while they depend on a more shallow architecture with the number of trained parameters being one order of magnitude smaller. These properties make the proposed networks ideal candidates to serve as sub-solvers on restoration methods that deal with general inverse imaging problems such as deblurring, demosaicking, superresolution, etc.Comment: Camera ready paper to appear in the Proceedings of CVPR 201

Models and Methods for Estimation and Filtering of Signal-Dependent Noise in Imaging

The work presented in this thesis focuses on Image Processing, that is the branch of Signal Processing that centers its interest on images, sequences of images, and videos. It has various applications: imaging for traditional cameras, medical imaging, e.g., X-ray and magnetic resonance imaging (MRI), infrared imaging (thermography), e.g., for security purposes, astronomical imaging for space exploration, three-dimensional (video+depth) signal processing, and many more.This thesis covers a small but relevant slice that is transversal to this vast pool of applications: noise estimation and denoising. To appreciate the relevance of this thesis it is essential to understand why noise is such an important part of Image Processing. Every acquisition device, and every measurement is subject to interferences that causes random fluctuations in the acquired signals. If not taken into consideration with a suitable mathematical approach, these fluctuations might invalidate any use of the acquired signal. Consider, for example, an MRI used to detect a possible condition; if not suitably processed and filtered, the image could lead to a wrong diagnosis. Therefore, before any acquired image is sent to an end-user (machine or human), it undergoes several processing steps. Noise estimation and denoising are usually parts of these fundamental steps.Some sources of noise can be removed by suitably modeling the acquisition process of the camera, and developing hardware based on that model. Other sources of noise are instead inevitable: high/low light conditions of the acquired scene, hardware imperfections, temperature of the device, etc. To remove noise from an image, the noise characteristics have to be first estimated. The branch of image processing that fulfills this role is called noise estimation. Then, it is possible to remove the noise artifacts from the acquired image. This process is referred to as denoising.For practical reasons, it is convenient to model noise as random variables. In this way, we assume that the noise fluctuations take values whose probabilities follow specific distributions characterized only by few parameters. These are the parameters that we estimate. We focus our attention on noise modeled by Gaussian distributions, Poisson distributions, or a combination of these. These distributions are adopted for modeling noise affecting images from digital cameras, microscopes, telescopes, radiography systems, thermal cameras, depth-sensing cameras, etc. The parameters that define a Gaussian distribution are its mean and its variance, while a Poisson distribution depends only on its mean, since its variance is equal to the mean (signal-dependent variance). Consequently, the parameters of a Poisson-Gaussian distribution describe the relation between the intensity of the noise-free signal and the variance of the noise affecting it. Degradation models of this kind are referred to as signal-dependent noise.Estimation of signal-dependent noise is commonly performed by processing, individually, groups of pixels with equal intensity in order to sample the aforementioned relation between signal mean and noise variance. Such sampling is often subject to outliers; we propose a robust estimation model where the noise parameters are estimated optimizing a likelihood function that models the local variance estimates from each group of pixels as mixtures of Gaussian and Cauchy distributions. The proposed model is general and applicable to a variety of signal-dependent noise models, including also possible clipping of the data. We also show that, under certain hypotheses, the relation between signal mean and noise variance can also be effectively sampled from groups of pixels of possibly different intensities.Then, we propose a spatially adaptive transform to improve the denoising performance of a specific class of filters, namely nonlocal transformdomain collaborative filters. In particular, the proposed transform exploits the spatial coordinates of nonlocal similar features from an image to better decorrelate the data, and consequently to improve the filtering. Unlike non-adaptive transforms, the proposed spatially adaptive transform is capable of representing spatially smooth coarse-scale variations in the similar features of the image. Further, based on the same paradigm, we propose a method that adaptively enhances the local image features depending on their orientation with respect to the relative coordinates of other similar features at other locations in the image.An established approach for removing Poisson noise utilizes so-called variance-stabilizing transformations (VST) to make the noise variance independent of the mean of the signal, hence enabling denoising by a standard denoiser for additive Gaussian noise. Within this framework, we propose an iterative method where at each iteration the previous estimate is summed back to the noisy image in order to improve the stabilizing performance of the transformation, and consequently to improve the denoising results. The proposed iterative procedure allows to circumvent the typical drawbacks that VSTs experience at very low intensities, and thus allows us to apply the standard denoiser effectively even at extremely low counts.The developed methods achieve state-of-the-art results in their respective field of application

The Secrets of Non-Blind Poisson Deconvolution

Non-blind image deconvolution has been studied for several decades but most of the existing work focuses on blur instead of noise. In photon-limited conditions, however, the excessive amount of shot noise makes traditional deconvolution algorithms fail. In searching for reasons why these methods fail, we present a systematic analysis of the Poisson non-blind deconvolution algorithms reported in the literature, covering both classical and deep learning methods. We compile a list of five "secrets" highlighting the do's and don'ts when designing algorithms. Based on this analysis, we build a proof-of-concept method by combining the five secrets. We find that the new method performs on par with some of the latest methods while outperforming some older ones.Comment: Under submission at Transactions on Computational Imagin

Poisson Noise Removal in Spherical Multichannel Images: Application to Fermi data

Chapitre 10International audienceThe aim of this chapter is to present a multi-scale representation for spherical data with Poisson noise called Multi-Scale Variance Stabilizing Transform on the Sphere (MS-VSTS) [14], combining the MS-VST [25] with various multi-scale transforms on the sphere (wavelets and curvelets) [22, 2, 3]. Section 1.2 presents some multi-scale transforms on the sphere. Section 1.3 introduces a new multi-scale representation for data with Poisson noise called MS-VSTS. Section 1.4 applies this representation to Poisson noise removal on Fermi data. Section 1.5 presents applications to missing data interpolation and source extraction. Section 1.6 extends the method to multichannel data