Compressed Sensing in Astronomy

Abstract

Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that provides an alternative to the well-known Shannon sampling theory. In this paper we investigate how compressed sensing (CS) can provide new insights into astronomical data compression and more generally how it paves the way for new conceptions in astronomical remote sensing. We first give a brief overview of the compressed sensing theory which provides very simple coding process with low computational cost, thus favoring its use for real-time applications often found on board space mission. We introduce a practical and effective recovery algorithm for decoding compressed data. In astronomy, physical prior information is often crucial for devising effective signal processing methods. We particularly point out that a CS-based compression scheme is flexible enough to account for such information. In this context, compressed sensing is a new framework in which data acquisition and data processing are merged. We show also that CS provides a new fantastic way to handle multiple observations of the same field view, allowing us to recover information at very low signal-to-noise ratio, which is impossible with standard compression methods. This CS data fusion concept could lead to an elegant and effective way to solve the problem ESA is faced with, for the transmission to the earth of the data collected by PACS, one of the instruments on board the Herschel spacecraft which will be launched in 2008.

30 pages - submitted to IEEE Journal on Selected Topics in Signal Processing

References in corpus (12)

• Rejoinder to "Least angle regression" by Efron et al
• Least Angle Regression
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Sparsity and Incoherence in Compressive Sampling
• Coded-Mask Imaging in Gamma-Ray Astronomy - Separating the Real and Imaginary parts of a Complex subject

Cited by in corpus (43)

• Compressive ghost imaging
• NESTA: A Fast and Accurate First-order Method for Sparse Recovery
• Multi-Scale CLEAN deconvolution of radio synthesis images
• Compressive Fluorescence Microscopy for Biological and Hyperspectral Imaging
• Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing
• Compressed sensing imaging techniques for radio interferometry
• Super sub-Nyquist single-pixel imaging by means of cake-cutting Hadamard basis sort
• Photon counting compressive depth mapping
• LOFAR Sparse Image Reconstruction
• Radial Velocity Data Analysis with Compressed Sensing Techniques
• Convolutional Compressed Sensing Using Deterministic Sequences
• Compressive Wavefront Sensing with Weak Values
• Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging
• Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging
• The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch
• A Compressed Sensing Approach to 3D Weak Lensing
• A multilevel based reweighting algorithm with joint regularizers for sparse recovery
• Sparse Representation of Astronomical Images
• Solar hard X-ray imaging by means of Compressed Sensing and Finite Isotropic Wavelet Transform
• 21cm Signal Recovery via the Robust Principle Component Analysis
• GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring
• Bayesian sparse reconstruction: a brute-force approach to astronomical imaging and machine learning
• Spatio-temporal Compressed Sensing with Coded Apertures and Keyed Exposures
• Effective implementation of $l_0$-Regularised Compressed Sensing with Chaotic-Amplitude-Controlled Coherent Ising Machines
• Rare-Allele Detection Using Compressed Se(que)nsing
• Feasibility and performances of compressed-sensing and sparse map-making with Herschel/PACS data
• Single-shot blind deconvolution with coded aperture
• EXIT Chart Analysis of Turbo Compressed Sensing Using Message Passing De-Quantization
• Compressive Coded Aperture Keyed Exposure Imaging with Optical Flow Reconstruction
• Simultaneous analysis of large INTEGRAL/SPI datasets: optimizing the computation of the solution and its variance using sparse matrix algorithms
• PARNES: A rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals
• Array imaging of localized objects in homogeneous and heterogeneous media
• Compressive Sensing with Redundant Dictionaries and Structured Measurements
• Modified lp-norm regularization minimization for sparse signal recovery
• Glancing Through Massive Binary Radio Lenses: Hardware-Aware Interferometry With 1-Bit Sensors
• Oblique Pursuits for Compressed Sensing
• Compressive Sensing for Polyharmonic Subdivision Wavelets With Applications to Image Analysis
• Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
• Bacterial Community Reconstruction Using A Single Sequencing Reaction
• Compressive Imaging and Characterization of Sparse Light Deflection Maps
• Outlier Detection Using Generative Models with Theoretical Performance Guarantees
• Analysis of non-stationary multicomponent signals with a focus on the Compressive Sensing approach
• Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry Property