Finding faint HI structure in and around galaxies: scraping the barrel

Soon to be operational HI survey instruments such as APERTIF and ASKAP will produce large datasets. These surveys will provide information about the HI in and around hundreds of galaxies with a typical signal-to-noise ratio of $\sim$ 10 in the inner regions and $\sim$ 1 in the outer regions. In addition, such surveys will make it possible to probe faint HI structures, typically located in the vicinity of galaxies, such as extra-planar-gas, tails and filaments. These structures are crucial for understanding galaxy evolution, particularly when they are studied in relation to the local environment. Our aim is to find optimized kernels for the discovery of faint and morphologically complex HI structures. Therefore, using HI data from a variety of galaxies, we explore state-of-the-art filtering algorithms. We show that the intensity-driven gradient filter, due to its adaptive characteristics, is the optimal choice. In fact, this filter requires only minimal tuning of the input parameters to enhance the signal-to-noise ratio of faint components. In addition, it does not degrade the resolution of the high signal-to-noise component of a source. The filtering process must be fast and be embedded in an interactive visualization tool in order to support fast inspection of a large number of sources. To achieve such interactive exploration, we implemented a multi-core CPU (OpenMP) and a GPU (OpenGL) version of this filter in a 3D visualization environment ($\tt{SlicerAstro}$).Comment: 17 pages, 9 figures, 4 tables. Astronomy and Computing, accepte

A hybrid neuro--wavelet predictor for QoS control and stability

For distributed systems to properly react to peaks of requests, their adaptation activities would benefit from the estimation of the amount of requests. This paper proposes a solution to produce a short-term forecast based on data characterising user behaviour of online services. We use \emph{wavelet analysis}, providing compression and denoising on the observed time series of the amount of past user requests; and a \emph{recurrent neural network} trained with observed data and designed so as to provide well-timed estimations of future requests. The said ensemble has the ability to predict the amount of future user requests with a root mean squared error below 0.06\%. Thanks to prediction, advance resource provision can be performed for the duration of a request peak and for just the right amount of resources, hence avoiding over-provisioning and associated costs. Moreover, reliable provision lets users enjoy a level of availability of services unaffected by load variations

State of the art in 2D content representation and compression

Livrable D1.3 du projet ANR PERSEECe rapport a été réalisé dans le cadre du projet ANR PERSEE (n° ANR-09-BLAN-0170). Exactement il correspond au livrable D3.1 du projet

Multiscale Adaptive Representation of Signals: I. The Basic Framework

We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational efficiency at inference time. It improves classical multi-scale basis such as wavelet frames in terms of coding efficiency. It provides an attractive alternative to dictionary learning-based techniques for low level signal processing tasks, such as compression and denoising, as well as high level tasks, such as feature extraction for object recognition. Connections with deep convolutional networks are also discussed. In particular, the proposed framework reveals a drawback in the commonly used approach for visualizing the activations of the intermediate layers in convolutional networks, and suggests a natural alternative

A PDE Approach to Data-driven Sub-Riemannian Geodesics in SE(2)

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group $SE(2) = \mathbb{R}^2 \rtimes S^1$ with a metric tensor depending on a smooth external cost $\mathcal{C}:SE(2) \to [\delta,1]$, $\delta>0$, computed from image data. The method consists of a first step where a SR-distance map is computed as a viscosity solution of a Hamilton-Jacobi-Bellman (HJB) system derived via Pontryagin's Maximum Principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. For $\mathcal{C}=1$ we show that our method produces the global minimizers. Comparison with exact solutions shows a remarkable accuracy of the SR-spheres and the SR-geodesics. We present numerical computations of Maxwell points and cusp points, which we again verify for the uniform cost case $\mathcal{C}=1$. Regarding image analysis applications, tracking of elongated structures in retinal and synthetic images show that our line tracking generically deals with crossings. We show the benefits of including the sub-Riemannian geometry.Comment: Extended version of SSVM 2015 conference article "Data-driven Sub-Riemannian Geodesics in SE(2)

Signal Denoising Method Based on Adaptive Redundant Second-Generation Wavelet for Rotating Machinery Fault Diagnosis

Vibration signal of rotating machinery is often submerged in a large amount of noise, leading to the decrease of fault diagnosis accuracy. In order to improve the denoising effect of the vibration signal, an adaptive redundant second-generation wavelet (ARSGW) denoising method is proposed. In this method, a new index for denoising result evaluation (IDRE) is constructed first. Then, the maximum value of IDRE and the genetic algorithm are taken as the optimization objective and the optimization algorithm, respectively, to search for the optimal parameters of the ARSGW. The obtained optimal redundant second-generation wavelet (RSGW) is used for vibration signal denoising. After that, features are extracted from the denoised signal and then input into the support vector machine method for fault recognition. The application result indicates that the proposed ARSGW denoising method can effectively improve the accuracy of rotating machinery fault diagnosis

AMM: Adaptive Multilinear Meshes

We present Adaptive Multilinear Meshes (AMM), a new framework that significantly reduces the memory footprint compared to existing data structures. AMM uses a hierarchy of cuboidal cells to create continuous, piecewise multilinear representation of uniformly sampled data. Furthermore, AMM can selectively relax or enforce constraints on conformity, continuity, and coverage, creating a highly adaptive and flexible representation to support a wide range of use cases. AMM supports incremental updates in both spatial resolution and numerical precision establishing the first practical data structure that can seamlessly explore the tradeoff between resolution and precision. We use tensor products of linear B-spline wavelets to create an adaptive representation and illustrate the advantages of our framework. AMM provides a simple interface for evaluating the function defined on the adaptive mesh, efficiently traversing the mesh, and manipulating the mesh, including incremental, partial updates. Our framework is easy to adopt for standard visualization and analysis tasks. As an example, we provide a VTK interface, through efficient on-demand conversion, which can be used directly by corresponding tools, such as VisIt, disseminating the advantages of faster processing and a smaller memory footprint to a wider audience. We demonstrate the advantages of our approach for simplifying scalar-valued data for commonly used visualization and analysis tasks using incremental construction, according to mixed resolution and precision data streams

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner