New strategies for avoiding robot joint limits: Application to visual servoing using a large projection operator

International audienceIn this paper, we present a new redundancy-based strategy for avoiding joint limits of a robot arm. This strategy is based on defining three functions for each joint: an activation function; an adaptive gain function; and a tuning function. These functions allow determining automatically the required sign and the suitable magnitude for the avoidance process at each joint. The problem of adding an additional task with the main task and the avoidance process is also considered and solved. As for the redundancy framework, a new large projection operator based on the norm of the usual error is used to enlarge the redundancy domain for applying our proposed avoidance strategy. The experimental results obtained on a 6 dof robot arm in eye-in hand visual servoing show that the new avoidance strategy gives smooth joint avoidance behavior without any tuning step. Using the new projection operator allows a significant improvement of the joint avoidance process, especially in the case of a full rank task function

PYRO-NN: Python Reconstruction Operators in Neural Networks

Purpose: Recently, several attempts were conducted to transfer deep learning to medical image reconstruction. An increasingly number of publications follow the concept of embedding the CT reconstruction as a known operator into a neural network. However, most of the approaches presented lack an efficient CT reconstruction framework fully integrated into deep learning environments. As a result, many approaches are forced to use workarounds for mathematically unambiguously solvable problems. Methods: PYRO-NN is a generalized framework to embed known operators into the prevalent deep learning framework Tensorflow. The current status includes state-of-the-art parallel-, fan- and cone-beam projectors and back-projectors accelerated with CUDA provided as Tensorflow layers. On top, the framework provides a high level Python API to conduct FBP and iterative reconstruction experiments with data from real CT systems. Results: The framework provides all necessary algorithms and tools to design end-to-end neural network pipelines with integrated CT reconstruction algorithms. The high level Python API allows a simple use of the layers as known from Tensorflow. To demonstrate the capabilities of the layers, the framework comes with three baseline experiments showing a cone-beam short scan FDK reconstruction, a CT reconstruction filter learning setup, and a TV regularized iterative reconstruction. All algorithms and tools are referenced to a scientific publication and are compared to existing non deep learning reconstruction frameworks. The framework is available as open-source software at \url{https://github.com/csyben/PYRO-NN}. Conclusions: PYRO-NN comes with the prevalent deep learning framework Tensorflow and allows to setup end-to-end trainable neural networks in the medical image reconstruction context. We believe that the framework will be a step towards reproducible researchComment: V1: Submitted to Medical Physics, 11 pages, 7 figure

Gauge Invariance and Spinon-Dopon Confinement in the t-J Model: implications for Fermi Surface Reconstruction in the Cuprates

We discuss the application of the two-band spin-dopon representation of the t-J model to address the issue of the Fermi surface reconstruction observed in the cuprates. We show that the electron no double occupancy (NDO) constraint plays a key role in this formulation. In particular, the auxiliary lattice spin and itinerant dopon degrees of freedom of the spin-dopon formulation of the t-J model are shown to be confined in the emergent U(1) gauge theory generated by the NDO constraint. This constraint is enforced by the requirement of an infinitely large spin-dopon coupling. As a result, the t-J model is equivalent to a Kondo-Heisenberg lattice model of itinerant dopons and localized lattice spins at infinite Kondo coupling at all dopings. We show that mean-field treatment of the large vs small Fermi surface crossing in the cuprates which leaves out the NDO constraint, leads to inconsistencies and it is automatically excluded form the t - J model framework

Gabor Shearlets

In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction. As a consequence, they can be implemented with standard filters from wavelet theory in combination with standard Gabor windows. Unlike the usual shearlets, the new construction can achieve a redundancy as close to one as desired. Our construction follows the general strategy for shearlets. First we define group-based Gabor shearlets and then modify them to a cone-adapted version. In combination with Meyer filters, the cone-adapted Gabor shearlets constitute a tight frame and provide low-redundancy sparse approximations of the common model class of anisotropic features which are cartoon-like functions.Comment: 24 pages, AMS LaTeX, 4 figure

Non-Redundant Spectral Dimensionality Reduction

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known as the "repeated Eigen-directions" phenomenon. That is, many of the embedding coordinates they produce typically capture the same direction along the data manifold. This leads to redundant and inefficient representations that do not reveal the true intrinsic dimensionality of the data. In this paper, we propose a general method for avoiding redundancy in spectral algorithms. Our approach relies on replacing the orthogonality constraints underlying those methods by unpredictability constraints. Specifically, we require that each embedding coordinate be unpredictable (in the statistical sense) from all previous ones. We prove that these constraints necessarily prevent redundancy, and provide a simple technique to incorporate them into existing methods. As we illustrate on challenging high-dimensional scenarios, our approach produces significantly more informative and compact representations, which improve visualization and classification tasks

Designing Gabor windows using convex optimization

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found