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Weak gravitational lensing is a very promising probe for cosmology that relies on highly precise shape measurements. Several new instruments are being deployed and will allow for weak lensing studies on unprecedented scales, and at new frequencies. In particular, some of these new instruments should allow for the blooming of radio-weak lensing, specially the SKA with many Petabits per second of raw data.1 Hence, great challenges will be waiting at the turn. In addition, processing methods should be able to extract the highest precision possible and ideally, be applicable to radio-astronomy. For the moment, the two methods that already exist do not satisfy both conditions. In this paper, we present a new plug-and-play solution where we add a shape constraint to deconvolution algorithms and results show measurements improvement of at least 20%.

International audience; Optimal Transport theory enables the definition of a distance across the set of measures on any given space. This Wasserstein distance naturally accounts for geometric warping between measures (including, but not exclusive to, images). We introduce a new, Optimal Transport-based representation learning method in close analogy with the usual Dictionary Learning problem. This approach typically relies on a matrix dot-product between the learned dictionary and the codes making up the new representation. The relationship between atoms and data is thus ultimately linear. By reconstructing our data as Wasserstein barycenters of learned atoms instead, our approach yields a representation making full use of the Wasserstein distance's attractive properties and allowing for non-linear relationships between the dictionary atoms and the datapoints. We apply our method to a dataset of Euclid-like simulated PSFs (Point Spread Function). ESA's Euclid mission will cover a large area of the sky in order to accurately measure the shape of billions of galaxies. PSF estimation and correction is one of the main sources of systematic errors on those galaxy shape measurements. PSF variations across the field of view and with the incoming light's wavelength can be highly non-linear, while still retaining strong geometrical information, making the use of Optimal Transport distances an attractive prospect. We show that our representation does indeed succeed at capturing the PSF's variations.

The future of far-infrared observations rests on our capacity to reach sub-arcsecond angular resolution around 100 μm, in order to achieve a significant advance with respect to our current capabilities. Furthermore, by reaching this angular resolution we can bridge the gap between capacities offered by the JWST in the near infrared and those allowed by ALMA in the submillimeter, and thus benefit from similar resolving capacities over the whole wavelength range where interstellar dust radiates and where key atomic and molecular transitions are found. In an accompanying paper,1 we present a concept of a deployable annular telescope, named TALC for Thinned Aperture Light Collector, reaching 20m in diameter. Being annular, this telescope features a main beam width equivalent to that of a 27m telescope, i.e. an angular resolution of 0.92" at 100 μm. In this paper we focus on the science case of such a telescope as well on the aspects of unconventional data processing that come with this unconventional optical configuration. The principal science cases of TALC revolve around its imaging capacities, that allow resolving the Kuiper belt in extra-solar planetary systems, or the filamentary scale in star forming clouds all the way to the Galactic Center, or the Narrow Line Region in Active Galactic Nuclei of the Local Group, or breaking the confusion limit to resolve the Cosmic Infrared Background. Equipping this telescope with detectors capable of imaging polarimetry offers as well the extremely interesting perspective to study the influence of the magnetic field in structuring the interstellar medium. We will then present simulations of the optical performance of such a telescope. The main feature of an annular telescope is the small amount of energy contained in the main beam, around 30% for the studied configuration, and the presence of bright diffraction rings. Using simulated point spread functions for realistic broad-band filters, we study the observing performance of TALC in typical situations, i.e a field of point sources, and fields with emission power at every physical scales, taken to represent an extragalactic deep field observation and an interstellar medium observation. We investigate different inversion techniques to try and recover the information present in the input field. We show that techniques combining a forward modeling of the observation process and a reconstruction algorithm exploiting the concept of sparsity (i.e. related to the more general field of compressed sensing) represent a promising avenue to reach the angular resolution promised by the main beam of TALC.

Active Range Imaging (ARI) has recently sparked an enthusiastic interest due to the numerous applications that can benefit from the high quality depth maps that ARI systems offer. One of the most successful ARI techniques employs Time-of-Flight (ToF) cameras which emit and subsequently record laser pulses in order to estimate the distance between the camera and objects in a scene. A limitation of this type of ARI is the requirement for a large number of frames that have to be captured in order to generate high resolution depth maps. In this work, we introduce Compressed Gated Range Sensing (CGRS), a novel approach for ToF-based ARI that utilizes the recently proposed framework of Compressed Sensing (CS) to dramatically reduce the number of necessary frames. The CGRS technique employs a random gating function along with state-of-the-art reconstruction in order to estimate the timing of a returning laser pulse and infer the depth map. To validate our method, software simulations were carried out using a realistic system model. Simulated results suggest that low error reconstruction of a depth map is possible using approximately 20% of the frames that traditional ToF cameras require, while 30% sampling rates can achieve very high fidelity reconstruction.

The LOFAR Radio Telescope is a radio interferometer with multiple antennas placed throughout Europe. A radio interferometer samples the image of the sky in the Fourier domain; recovering the image from these samples is an inverse problem. In radio astronomy the CLEAN method has been used for many years to find a solution. Recent papers have established a link between radio interferometry and compressed sensing, which supports sparse recovery methods to reconstruct an image from interferometric data. The goal of this paper is to study sparse recovery methods on LOFAR data by comparing the accuracy of CLEAN and compressed sensing when applied to simulated LOFAR observations.

We propose a new method to better estimate and subtract the contribution of detected compact sources to the microwave sky. These bright compact source emissions contaminate the full-sky data over a significant fraction of the sky, and should therefore be accurately removed if a high resolution and full-sky estimate of the components is sought after. However the point source spectral variability hampers accurate blind source separation, even with state-of-the-art localized source separation techniques. In this work, we rather propose to estimate the flux of the brightest compact sources using a morphological separation approach, relying on a more sophisticated model for the background than in standard approaches. Essentially, this amounts to separate point sources with known support and shape from a background assumed sparse in the spherical harmonic domain. This approach is compared to standard local χ 2 minimization modeling the background as a low order polynomial on WMAP realistic simulations. If in noisy situations estimating more than a few parameter does not improve flux recovery, in the first WMAP channels the proposed method leads to lower biases (typically by factors of 2) and increased robustness.

We present an application of sparse regularization of ill-posed linear inverse problems to the reconstruction of the 3D distribution of dark matter in the Universe. By its very nature dark matter cannot be directly observed. Nevertheless, it can be studied through its gravitational effects can it be studied. In particular, the presence of dark matter induces small deformations to the shapes of background galaxies which is known as weak gravitational lensing. However, reconstructing the 3D distribution of dark matter from tomographic lensing measurements amounts to solving an ill-posed linear inverse problem. Considering that the 3D dark matter density is sparse in an appropriate wavelet based 3D dictionary, we propose an iterative thresholding algorithm to solve a penalized least-squares problem. We present our results on simulated dark matter halos and compare them to state of the art linear reconstruction techniques. We show that thanks to our 3D sparsity constraint the quality of the reconstructed maps can be greatly improved.

We present several 3D sparse decompositions based on wavelets on the sphere that are useful for different kind of data set such as regular 3D spherical measurements (r,θ, φ) and multichannel spherical measurements (λ, θ, φ). We show how these new decompositions can be used for astronomical data denoising and deconvolution, when the data are contaminated by Gaussian and Poisson noise.

In this paper, we introduce a method to stabilize the variance of decimated transforms using one or two variance stabilizing transforms (VST). These VSTs are applied to the 3-D Meyer wavelet pyramidal transform which is the core of the first generation 3D curvelets. This allows us to extend these 3-D curvelets to handle Poisson noise, that we apply to the denoising of a simulated cosmological volume.

Range Imaging (RI) has sparked an enthusiastic interest recently due to the numerous applications that can benefit from the presence 3D data. One of the most successful techniques for RI employs Time-of-Flight (ToF) cameras which emit and subsequently record laser pulses in order to estimate the distance between the camera and an object. A limitation of this class of RI is the requirement for a large number of frames that have to be captured in order to generate high resolution depth maps. In this work, we propose a novel approach for ToF based RI that utilizes the recently proposed framework of Compressed Sensing to dramatically reduce the number of necessary frames. Our technique employs a random gating function along with state-of-the-art minimization techniques in order to estimate the location of a returning laser pulse and infer the distance. To validate the theoretical motivation, software simulations were carried out. Our simulated results have shown that reconstruction of a depth map is possible from as low as 10% of the frames that traditional ToF cameras require with minimum reconstruction error while 20% sampling rates can achieve almost perfect reconstruction in low resolution regimes. Our experimental results have also shown that the proposed method is robust to various types of noise and applicable to realistic signal models.

We develop a wavelet transform on the sphere, based on the spherical HEALPix coordinate system (Hierarchical Equal Area iso-Latitude Pixelization). HEALPix is heavily used for astronomical data processing applications; it is intrinsically multiscale and locally euclidean, hence appealing for building multiscale system. Furthermore, the equal-area pixelization enables us to employ average-interpolating refinement, giving wavelets of local support. HEALPix wavelets have numerous applications in geopotential modeling. A statistical analysis demonstrates wavelet compressibility of the geopotential field and shows that geopotential wavelet coefficients have many of the statistical properties that were previously observed with wavelet coefficients of natural images. The HEALPix wavelet expansion allows to evaluate a gravimetric quantity over a local region far more rapidly than the classic approach based on spherical harmonics. Our software tools are specifically tailored to demonstrate these advantages.

International audience; This article proposes a new method for image separation into a linear combination of morphological components. This method is applied to decompose an image into meaningful cartoon and textural layers and is used to solve more general inverse problems such as image inpainting. For each of these components, a dictionary is learned from a set of exemplar images. Each layer is characterized by a sparse expansion in the corresponding dictionary. The separation inverse problem is formalized within a variational framework as the optimization of an energy functional. The morphological component analysis algorithm allows to solve iteratively this optimization problem under sparsity-promoting penalties. Using adapted dictionaries learned from data allows to circumvent some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial to capture complex texture patterns.

The statistics of the temperature anisotropies in the primordial Cosmic Microwave Background radiation field provide a wealth of information for cosmology and the estimation of cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the latter extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence awaited with excitement. Still, analyzing CMB data requires tackling a number of practical difficulties, notably that several other astrophysical sources emit radiation in the frequency range of CMB observations. Separating the different astrophysical foreground components and the CMB proper from available multichannel data is a problem that has drawn much attention in the community. Nevertheless, some level of residual contributions, most significantly in the galactic region and at the locations of strong radio point sources will unavoidably contaminate the estimated spherical CMB map. Masking out these regions is common practice but the gaps in the data need proper handling. In order to restore the stationarity of a partly incomplete CMB map and thus lower the impact of the gaps on non-local statistical tests, we developed an inpainting algorithm on the sphere to fill in the gaps, based on an iterative thresholding scheme in a sparse representation of the data. This algorithm relies on the variety of recently developed transforms on the sphere among which several multiscale transforms which we will review. We also contribute to enlarging the set of available transforms for polarized data on the sphere. We describe new multiscale decompositions namely the isotropic undecimated wavelet and curvelet transforms for polarized data on the sphere. The proposed transforms are invertible and so allow for applications in image restoration and denoising.

The Morphological Component Analysis (MCA) is a a new method which allows us to separate features contained in an image when these features present different morphological aspects. We show that MCA can be very useful for decomposing images into texture and piecewise smooth (cartoon) parts or for inpainting applications. We extend MCA to a multichannel MCA (MMCA) for analyzing multispectral data and present a range of examples which illustrates the results.

Analyzing data mapped to the sphere as may occur in a range of applications in geophysics, medical imaging or astrophysics, requires specific tools. This paper describes new multiscale decompositions for spherical images namely the isotropic undecimated wavelet transform, the ridgelet transform and the curvelet transform each of which is invertible. Several applications are described. We show how these transforms can be used in denoising and especially in a Combined Filtering Method, which uses both the wavelet and the curvelet transforms, thus benefiting from the advantages of both transforms. An application to component separation from multichannel data mapped to the sphere is also described where we take advantage of the spatiospectral localization on the sphere provided by the spherical wavelet functions.

The design and successful fielding of sensors and detectors vital for homeland security can benefit greatly by the use of advanced signal and image processing techniques. The intent is to extract as much reliable information as possible despite noisy and hostile environments where the signals and images are gathered. In addition, the ability to perform fast analysis and response necessitate significant compression of the raw data so that they may be efficiently transmitted, remotely accumulated from different sources, and processed. Proper decompositions into compact representations allow fast pattern detection and pattern matching in real time, in situ or otherwise. Wavelets for signals and curvelets for images or hyperspectral data promise to be of paramount utility in the implementation of these goals. Together with statistical modeling and iterative thresholding techniques, wavelets, curvelets and multiresolution analysis can alleviate the severity of the requirements which today’s hardware designs can not meet in order to measure trace levels of toxins and hazardous substances. Photonic or electrooptic sensor and detector designs of the future, for example, must take into account the end game strategies made available by advanced signal and image processing techniques. The promise is the successful operation at lower signal to noise ratios, with less data mass and with deeper statistical inferences made possible than with boxcar or running averaging techniques (low pass filtering) much too commonly used to deal with noisy data at present. SPREE diagrams (spectroscopic peak reconstruction error estimation) are introduced in this paper to facilitate the decision of which wavelet filter and which denoising scheme to use with a given noisy data set.

Z pinches produce an X ray rich plasma environment where backlighting imaging of imploding targets can be quite challenging to analyze. What is required is a detailed understanding of the implosion dynamics by studying snapshot images of its in flight deformations away from a spherical shell. We have used wavelets, curvelets and multiresolution analysis techniques to address some of these difficulties and to establish the Shell Thickness Averaged Radius (STAR) of maximum density, r*(N, {\theta}), where N is the percentage of the shell thickness over which we average. The non-uniformities of r*(N, {\theta}) are quantified by a Legendre polynomial decomposition in angle, {\theta}, and the identification of its largest coefficients. Undecimated wavelet decompositions outperform decimated ones in denoising and both are surpassed by the curvelet transform. In each case, hard thresholding based on noise modeling is used., Comment: 11 pages, 17 figures, Volume 5207 Wavelets: Applications in Signal and Image Processing X. 10.1117/12.506243

Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy distribution and discriminate the different cosmological models. We present in this paper preliminary results relative to the use of new statistical tools using the 3D a trous algorithm, the 3D ridgelet transform and the 3D beamlet transform. We show that such multiscale methods produce a new way to measure in a coherent and statistically reliable way the degree of clustering, filamentarity, sheetedness, and voidedness of a dataset.

We have developed tools for analysis of 3D volumetric data which allow sensitive characterizations of filamentary structures in 3D point clouds. These tools rapidly compute multiscale X-ray transforms of the data volume. Subcubes of varying locations and scales are extracted from the data volume and each is analyzed by integrating along a strategically chosen set of line segments covering all different orientations. The underlying motivation is that point clouds with different degrees of filamentarity will lead to multiscale X-ray coefficients having different distributions when viewed at the right scale. The multiscale approach guarantees that information from all scales is available; by extracting the information from the transform in a statistically appropriate fashion, we can sensitively resolve differences in details of the filamentarity. We will describe the algorithm and the results of comparing different simulated galaxy distributions.

One of the goals in cosmology is to understand the formation and evolution of the structures resulting from the growth of initial density perturbations. Recent Cosmic Microwave Background (CMB)observations indicate that these pertubations essentially came out of Gaussian distributed quantum fluctuations in the inflationary scenario. However, topological defects (e.g. cosmic strings) could contribute to the signal. One of their important footprints would be the predicted non-Gaussian distribution of the temperature anisotropies. In addition, other sources of non-Gaussian signatures do contribute to the signal, in particular the Sunyaev-Zel'dovich effect of galaxy clusters. In this general context and motivated by the future CMB experiments, the question we address is to search for, and discriminate between, different non-Gaussian signatures. To do so, we analyze simulated maps of the CMB temperature anisotropies using both wavelet and curvelet transforms. Curvelets take the form of basis elements which exhibit very high directional sensitivity and are highly anisotropic, which is not the case for wavelets. The sensitivity of both methods is evaluated using simulated data sets.

We outline digital implementations of two newly developed multiscale representation systems, namely, the ridgelet and curvelet transforms. We apply these digital transforms to the problem of restoring an image from noisy data and compare our results with those obtained via well established methods based on the thresholding of wavelet coefficients. We develop a methodology to combine wavelets together these new systems to perform noise removal by exploiting all these systems simultaneously. The results of the combined reconstruction exhibits clear advantages over any individual system alone. For example, the residual error contains essentially no visually intelligible structure: no structure is lost in the reconstruction.

Many multiscale methods have been developed during the last fifteen years, such the bi-orthogonal wavelet transform, the \`a trous algorithm, the ridgelet transform or the curvelet transform. Each of them is optimal to detect one kind of features. We present the Combined Transforms Method which allows us to combine several transformations in order to benefit of the advantages of each of them.

Performance results using wavelet and other multiresolution transforms are described. The roles of information content, resolution scale, and image capture noise, are discussed. Delivery systems for a range of large image repositories from areas which include medical, astronomy and graphic arts are described, as standalone systems for use on portable platforms, and client-server systems for use on the web.

In the so-called parallel mode, ISOCAM, the mid-infrared camera on board ESA's Infrared Space Observatory (ISO), continued to observe while other instruments were prime, thus providing a widespread high-sensitivity survey of the sky. The currently exploitable data set was taken during 7000 hours of observations and consists of over 37000 pointings. The source extraction from these images is a challenging task due to the following difficulties: * the small number of pixels per image (32*32), resulting into a highly under-sampled Point Spread Function * the varying sky area --- from flat background to highly structured or confused * the varying and a priori unknown instrumental noise and the highly varying duration of each pointing * the high number of spurious sources due to restricted glitch-rejection for observations with few readouts * the lack of redundant pointings for the majority of cases The algorithm developed to solve these problems consists of a combination of three detection methods: * sextractor, using various thresholds and convolution files * multi-resolution detection * flux- and position determination of detected sources via modified point-source fitting * heuristic criteria to classify the sources into point- and extended sources© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We introduce in this paper the notion of WT-KLT and apply it to the problem of noise removal. Decorrelating first the data in the spatial domain using the WT and afterwards using the KLT in spectral domain allows us to derive a roust noise modeling in the WT-KLT space, and hence to filter the transformed data in an efficient way. Experiments are performed in order to derive (i) the best way to calculate the covariance matrix in the case of noisy data, (ii) the best method to correct the noisy WT-KLT coefficients. Finally we investigate if the curvelet transform could be an alternative to the wavelet transform for color image filtering.

We present in this paper a new way to measure the information in a signal, based on noise modeling. We show that the use of such an entropy-related measure leads to good results for signal restoration.

We use an automatic re-registering of frames taken from a surveillance video to improve signal-to-noise in regions of particular interest. A wavelet transform with automatic signal and noise estimation is used for this purpose. We describe the results obtained using a short surveillance video sequence.

In 1994, to overcome the difficulties encountered by the maximum entropy method (MEM) to restore images containing both high and low frequencies, Bonteoke et al. introduced the Pyramid Maximum Entropy Deconvolution. However, this method presents several drawbacks such as parameters estimation (model, alpha). Furthermore, in their method they don't minimize any functional. Following these ideas, we propose the multiresolution maximum entropy method which is based on the concept of multiscale entropy derived from the wavelet decomposition of a signal into different frequency bands. It leads to a method which is flux conservative, and the use of a multiresolution support solves the problem of MEM to choose the (alpha) parameter, i.e. relative weight between the goodness-of-fit and the entropy. We also show that our algorithm is efficient for filtering astronomical images.

An algorithm is described which simulates atmospherically distorted wavefronts using a Zernike expansion of randomly weighted Karhunen-Loeve functions. Its performance are presented and analyzed thereafter. The program is then used to forecast resulting structure function and Strehl resolution for adaptive optics systems.

The advent of large format CCD detectors and of dedicated survey telescopes is providing the astronomical community with datasets of unprecedented size and quality. These data sets cannot be effectively exploited with traditional interactive tools and require the use of innovative data mining and visualization tools resulting from a synergy between astronomy and information sciences. We discuss here some preliminary results obtained by our group in the fields of automatic clustering in multiparametric space and detection of time transients (both astrometric and photometric).