Adaptive multiresolution analysis based on synchronization

We propose an adaptive multiscale approach to data analysis based on synchronization. The approach is nonlinear, data driven in the sense that it does not rely on a priori chosen basis, and automatically determines the data scale. Numerical results for one- and two-dimensional cases illustrate that the method works effectively for the usual modulated signals such as chirps, etc., as well as for more complicated data with multiple scales. The method extends straightforwardly to functions defined on weighted graphs and grids in high dimensions. Connections with some other recent approaches to multiscale analysis are briefly discussed

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

High-Dimensional Data Reduction, Image Inpainting and their Astronomical Applications

Technological advances are revolutionizing multispectral astrophysics as well as the detection and study of transient sources. This new era of multitemporal and multispectral data sets demands new ways of data representation, processing and management thus making data dimension reduction instrumental in efficient data organization, retrieval, analysis and information visualization. Other astrophysical applications of data dimension reduction which require new paradigms of data analysis include knowledge discovery, cluster analysis, feature extraction and object classification, de-correlating data elements, discovering meaningful patterns and finding essential representation of correlated variables that form a manifold (e.g. the manifold of galaxies), tagging astronomical images, multiscale analysis synchronized across all available wavelengths, denoising, etc. The second part of this paper is dedicated to a new, active area of image processing: image inpainting that consists of automated methods for filling in missing or damaged regions in images. Inpainting has multiple astronomical applications including restoring images corrupted by instrument artifacts, removing undesirable objects like bright stars and their halos, sky estimating, and pre-processing for the Fourier or wavelet transforms. Applications of high-dimensional data reduction and mitigation of instrument artifacts are demonstrated on images taken by the Spitzer Space Telescope

Multiscale Astronomical Image Processing Based on Nonlinear Partial Differential Equations

Astronomical applications of recent advances in the field of nonastronomical image processing are presented. These innovative methods, applied to multiscale astronomical images, increase signal-to-noise ratio, do not smear point sources or extended diffuse structures, and are thus a highly useful preliminary step for detection of different features including point sources, smoothing of clumpy data, and removal of contaminants from background maps. We show how the new methods, combined with other algorithms of image processing, unveil fine diffuse structures while at the same time enhance detection of localized objects, thus facilitating interactive morphology studies and paving the way for the automated recognition and classification of different features. We have also developed a new application framework for astronomical image processing that implements some recent advances made in computer vision and modern image processing, along with original algorithms based on nonlinear partial differential equations. The framework enables the user to easily set up and customize an image-processing pipeline interactively; it has various common and new visualization features and provides access to many astronomy data archives. Altogether, the results presented here demonstrate the first implementation of a novel synergistic approach based on integration of image processing, image visualization, and image quality assessment

Neuronal synchronization and multiscale information processing

Many important processes in neurobiology as well as neuronal engineering applications rely upon multiresolution representation and analysis of external information. There are various approaches which attempt to explain how human perception systems perform multiscale representation and sparse coding. The model proposed here is based on a new approach to multiresolution of input signals and reveals synchronization as a general mechanism for multiscale representation common to various sensory systems. The proposed mechanism is nonlinear and adaptive in the sense that it does not rely on convolution with a preconceived basis. For the visual system this approach is a major departure from the current linear paradigm, which holds that the structure of the receptive fields and their variations are responsible for performing multiscale analysis. While there are some well-known, important roles played by entrainment in neuronal systems, our model reveals a new function of dynamic coordination in the brain - multiscale encoding, thus demonstrating that synchronization plays a greater role in perception in general and in vision in particular, than was previously thought

Spitzer Space Telescope MIPS Germanium Pipeline

The MIPS Germanium data reduction pipelines present challenges to remove a wide variety of detector artifacts and still operate efficiently in a loosely coupled multiprocessor environment. The system scheduling architecture is designed to sequentially execute four stages of pipelines. Each pipeline stage is built around perl scripts that can invoke Fortran/C/C++ modules or Informix database stored procedures. All inter-pipeline communication is via the database. The pipeline stages are the elimination of nonlinear and radiation artifacts in the flux measurement, the calibration of the fluxes with both onboard and stellar calibration sources, applying post-facto pointing information, and assembling individual exposures into mosaics

Image Processing Application for Cognition: IPAC Architecture and Implementation in Java

An application framework for advanced image processing and visualization is presented. It provides common two-dimensional operators and implements recent developments in the field of image processing as well as original algorithms based on nonlinear partial differential equations (PDEs). It is platform independent and has the capability of extensibility. This objective is achieved by exploiting the object-oriented paradigm. A graphical user interface (GUI) provides processing, analysis and visualization in a highly integrated, easy to use environment. Applications of the developed system to images obtained by the Spitzer Space Telescope are demonstrated

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page