Detection and Characterization of Exoplanets and Disks using Projections on Karhunen-Loeve Eigenimages

We describe a new method to achieve point spread function (PSF) subtractions for high- contrast imaging using Principal Component Analysis (PCA) that is applicable to both point sources or extended objects (disks). Assuming a library of reference PSFs, a Karhunen-Lo`eve transform of theses references is used to create an orthogonal basis of eigenimages, on which the science target is projected. For detection this approach provides comparable suppression to the Locally Optimized Combination of Images (LOCI) algorithm, albeit with increased robustness to the algorithm parameters and speed enhancement. For characterization of detected sources the method enables forward modeling of astrophysical sources. This alleviates the biases in the astrometry and photometry of discovered faint sources, which are usually associated with LOCI- based PSF subtractions schemes. We illustrate the algorithm performance using archival Hubble Space Telescope (HST) images, but the approach may also be considered for ground-based data acquired with Angular Differential Imaging (ADI) or integral-field spectrographs (IFS).Comment: 12 pages, 4 figure

The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy

Classification accuracy increase using multisensor data fusion

The practical use of very high resolution visible and near-infrared (VNIR) data is still growing (IKONOS, Quickbird, GeoEye-1, etc.) but for classification purposes the number of bands is limited in comparison to full spectral imaging. These limitations may lead to the confusion of materials such as different roofs, pavements, roads, etc. and therefore may provide wrong interpretation and use of classification products. Employment of hyperspectral data is another solution, but their low spatial resolution (comparing to multispectral data) restrict their usage for many applications. Another improvement can be achieved by fusion approaches of multisensory data since this may increase the quality of scene classification. Integration of Synthetic Aperture Radar (SAR) and optical data is widely performed for automatic classification, interpretation, and change detection. In this paper we present an approach for very high resolution SAR and multispectral data fusion for automatic classification in urban areas. Single polarization TerraSAR-X (SpotLight mode) and multispectral data are integrated using the INFOFUSE framework, consisting of feature extraction (information fission), unsupervised clustering (data representation on a finite domain and dimensionality reduction), and data aggregation (Bayesian or neural network). This framework allows a relevant way of multisource data combination following consensus theory. The classification is not influenced by the limitations of dimensionality, and the calculation complexity primarily depends on the step of dimensionality reduction. Fusion of single polarization TerraSAR-X, WorldView-2 (VNIR or full set), and Digital Surface Model (DSM) data allow for different types of urban objects to be classified into predefined classes of interest with increased accuracy. The comparison to classification results of WorldView-2 multispectral data (8 spectral bands) is provided and the numerical evaluation of the method in comparison to other established methods illustrates the advantage in the classification accuracy for many classes such as buildings, low vegetation, sport objects, forest, roads, rail roads, etc

The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points characterized by a fixed stregth of the singularity of the contrast gradient in its neighborhood. A crucial role in this description of images is played by the behavior of contrast differences under changes in scale. Contrary to naive scaling ideas where the image is thought to have uniform transformation properties \cite{Fie87}, each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.Comment: 41 pages, 8 figures, LaTe