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

Template matching method for the analysis of interstellar cloud structure

The structure of interstellar medium can be characterised at large scales in terms of its global statistics (e.g. power spectra) and at small scales by the properties of individual cores. Interest has been increasing in structures at intermediate scales, resulting in a number of methods being developed for the analysis of filamentary structures. We describe the application of the generic template-matching (TM) method to the analysis of maps. Our aim is to show that it provides a fast and still relatively robust way to identify elongated structures or other image features. We present the implementation of a TM algorithm for map analysis. The results are compared against rolling Hough transform (RHT), one of the methods previously used to identify filamentary structures. We illustrate the method by applying it to Herschel surface brightness data. The performance of the TM method is found to be comparable to that of RHT but TM appears to be more robust regarding the input parameters, for example, those related to the selected spatial scales. Small modifications of TM enable one to target structures at different size and intensity levels. In addition to elongated features, we demonstrate the possibility of using TM to also identify other types of structures. The TM method is a viable tool for data quality control, exploratory data analysis, and even quantitative analysis of structures in image data.Comment: 12 pages, accepted to A&

Graph Regularized Tensor Sparse Coding for Image Representation

Sparse coding (SC) is an unsupervised learning scheme that has received an increasing amount of interests in recent years. However, conventional SC vectorizes the input images, which destructs the intrinsic spatial structures of the images. In this paper, we propose a novel graph regularized tensor sparse coding (GTSC) for image representation. GTSC preserves the local proximity of elementary structures in the image by adopting the newly proposed tubal-tensor representation. Simultaneously, it considers the intrinsic geometric properties by imposing graph regularization that has been successfully applied to uncover the geometric distribution for the image data. Moreover, the returned sparse representations by GTSC have better physical explanations as the key operation (i.e., circular convolution) in the tubal-tensor model preserves the shifting invariance property. Experimental results on image clustering demonstrate the effectiveness of the proposed scheme

Evidence for parallel elongated structures in the mesosphere

The physical cause of partial reflection from the mesosphere is of interest. Data are presented from an image-forming radar at Brighton, Colorado, that suggest that some of the radar scattering is caused by parallel elongated structures lying almost directly overhead. Possible physical sources for such structures include gravity waves and roll vortices

CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization

This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of \cite{Dong2013X} and that of the data-driven tight frames for image denoising \cite{cai2014data}. It is different from existing models in that both CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments showed that the SRD-DDTF model is superior to the model by \cite{Dong2013X} especially in recovering some subtle structures in the images

img2net: Automated network-based analysis of imaged phenotypes

Automated analysis of imaged phenotypes enables fast and reproducible quantification of biologically relevant features. Despite recent developments, recordings of complex, networked structures, such as: leaf venation patterns, cytoskeletal structures, or traffic networks, remain challenging to analyze. Here we illustrate the applicability of img2net to automatedly analyze such structures by reconstructing the underlying network, computing relevant network properties, and statistically comparing networks of different types or under different conditions. The software can be readily used for analyzing image data of arbitrary 2D and 3D network-like structures. img2net is open-source software under the GPL and can be downloaded from http://mathbiol.mpimp-golm.mpg.de/img2net/, where supplementary information and data sets for testing are provided.Comment: Bioinformatics, 2014, btu50