Meyer Z. Pesenson

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.

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 in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments that are vital to the analysis and visualization of complex datasets and images. One of the goals of this paper is to help bridge the gap between applied mathematics and artificial intelligence on the one side and astronomy on the other.

Approximation of Besov Vectors by Paley–Wiener Vectors in Hilbert Spaces

We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data representation, compression, denoising and visualization. These tasks are of great importance to machine learning, complex data analysis and computer vision.

High Throughput Combinatorial Experimentation + Informatics = Combinatorial Science

Many present, emerging and future technologies rely upon the development high performance functional materials. For a given application, the performance of materials containing 1 or 2 elements from the periodic table have been evaluated using traditional techniques, and additional materials complexity is required to continue the development of advanced materials, for example through the incorporation of several elements into a single material. The combinatorial aspect of combining several elements yields vast composition spaces that can be effectively explored with high throughput techniques. State of the art high throughput experiments produce data which are multivariate, high-dimensional, and consist of wide ranges of spatial and temporal scales. We present an example of such data in the area of water splitting electrocatalysis and describe recent progress on 2 areas of interpreting such vast, complex datasets. We discuss a genetic programming technique for automated identification of composition-property trends, which is important for understanding the data and crucial in identifying representative compositions for further investigation. By incorporating such an algorithm in a high throughput experimental pipeline, the automated down-selection of samples can empower a highly efficient tiered screening platform. We also discuss some fundamental mathematics of composition spaces, where compositional variables are non-Euclidean due to the constant-sum constraint. We describe the native simplex space spanned by composition variables and provide illustrative examples of statistics and interpolation within this space. Through further development of machine learning algorithms and their prudent implementation in the simplex space, the data informatics community will establish methods that derive the most knowledge from high throughput materials science data.

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.