Invariant descriptor learning using a Siamese convolutional neural network

In this paper we describe learning of a descriptor based on the Siamese Convolutional Neural Network (CNN) architecture and evaluate our results on a standard patch comparison dataset. The descriptor learning architecture is composed of an input module, a Siamese CNN descriptor module and a cost computation module that is based on the L2 Norm. The cost function we use pulls the descriptors of matching patches close to each other in feature space while pushing the descriptors for non-matching pairs away from each other. Compared to related work, we optimize the training parameters by combining a moving average strategy for gradients and Nesterov's Accelerated Gradient. Experiments show that our learned descriptor reaches a good performance and achieves state-of-art results in terms of the false positive rate at a 95% recall rate on standard benchmark datasets

Fast distributed first-order methods

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 91-94).This thesis provides a systematic framework for the development and analysis of distributed optimization methods for multi-agent networks with time-varying connectivity. The goal is to optimize a global objective function which is the sum of local objective functions privately known to individual agents. In our methods, each agent iteratively updates its estimate of the global optimum by optimizing its local function and exchanging estimates with others in the network. We introduce distributed proximal-gradient methods that enable the use of a gradient-based scheme for non-differentiable functions with a favorable structure. We present a convergence rate analysis that highlights the dependence on the step size rule. We also propose a novel fast distributed method that uses Nesterov-type acceleration techniques and multiple communication steps per iteration. Our method achieves exact convergence at the rate of O(1/t) (where t is the number of communication steps taken), which is superior than the rates of existing gradient or subgradient algorithms, and is confirmed by simulation results.by I-An Chen.S.M

Nonsmooth Algorithms and Nesterov\u27s Smoothing Technique for Generalized Fermat-Torricelli Problems

We present algorithms for solving a number of new models of facility location which generalize the classical Fermat--Torricelli problem. Our first approach involves using Nesterov\u27s smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms

On the generalized langevin equation for simulated annealing

In this paper, we consider the generalized (higher order) Langevin equation for the purpose of simulated annealing and optimization of nonconvex functions. Our approach modifies the underdamped Langevin equation by replacing the Brownian noise with an appropriate Ornstein–Uhlenbeck process to account for memory in the system. Under reasonable conditions on the loss function and the annealing schedule, we establish convergence of the continuous time dynamics to a global minimum. In addition, we investigate the performance numerically and show better performance and higher exploration of the state space compared to the underdamped Langevin dynamics with the same annealing schedule

Low-rank and sparse reconstruction in dynamic magnetic resonance imaging via proximal splitting methods

Dynamic magnetic resonance imaging (MRI) consists of collecting multiple MR images in time, resulting in a spatio-temporal signal. However, MRI intrinsically suffers from long acquisition times due to various constraints. This limits the full potential of dynamic MR imaging, such as obtaining high spatial and temporal resolutions which are crucial to observe dynamic phenomena. This dissertation addresses the problem of the reconstruction of dynamic MR images from a limited amount of samples arising from a nuclear magnetic resonance experiment. The term limited can be explained by the approach taken in this thesis to speed up scan time, which is based on violating the Nyquist criterion by skipping measurements that would be normally acquired in a standard MRI procedure. The resulting problem can be classified in the general framework of linear ill-posed inverse problems. This thesis shows how low-dimensional signal models, specifically lowrank and sparsity, can help in the reconstruction of dynamic images from partial measurements. The use of these models are justified by significant developments in signal recovery techniques from partial data that have emerged in recent years in signal processing. The major contributions of this thesis are the development and characterisation of fast and efficient computational tools using convex low-rank and sparse constraints via proximal gradient methods, the development and characterisation of a novel joint reconstruction–separation method via the low-rank plus sparse matrix decomposition technique, and the development and characterisation of low-rank based recovery methods in the context of dynamic parallel MRI. Finally, an additional contribution of this thesis is to formulate the various MR image reconstruction problems in the context of convex optimisation to develop algorithms based on proximal splitting methods

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal