Sparse Representation of Astronomical Images

Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm: i)Effectiveness at producing sparse representations. ii)Competitiveness, with respect to the time required to process large images.The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks.This feature makes it possible to apply the effective greedy selection technique Orthogonal Matching Pursuit, up to some block size. For blocks exceeding that size a refinement of the original Matching Pursuit approach is considered. The resulting method is termed Self Projected Matching Pursuit, because is shown to be effective for implementing, via Matching Pursuit itself, the optional back-projection intermediate steps in that approach.Comment: Software to implement the approach is available on http://www.nonlinear-approx.info/examples/node1.htm

Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data

The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape

Recognition of human body posture from a cloud of 3D data points using wavelet transform coefficients

Addresses the problem of recognizing a human body posture from a cloud of 3D points acquired by a human body scanner. Motivated by finding a representation that embodies a high discriminatory power between posture classes, a new type of feature is suggested, namely the wavelet transform coefficients (WTC) of the 3D data-point distribution projected on to the space of spherical harmonics. A feature selection technique is developed to find those features with high discriminatory power. Integrated within a Bayesian classification framework and compared with other standard features, the WTC showed great capability in discriminating between close postures. The qualities of the WTC features were also reflected in the experimental results carried out with artificially generated postures, where the WTC obtained the best classification rat

Progressive construction of a parametric reduced-order model for PDE-constrained optimization

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given Reduced-Order Model (ROM) is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the High-Dimensional Model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust-region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a Reduced-Order Basis (ROB) is also presented, along with a methodology for computing sensitivities of the reduced-order model that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4-5, compared to the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1%

Constructing an overall dynamical model for a system with changing design parameter properties

This study considers the identification problem for a class of non-linear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient Common Model Structure Selection (CMSS) algorithm, called the Extended Forward Orthogonal Regression (EFOR) algorithm, is proposed to select such a common model structure. Two examples are presented to illustrate the application and the effectiveness of the new identification approach

Localized Manifold Harmonics for Spectral Shape Analysis

The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases