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The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for imaging inverse problems, namely deconvolution and reconstruction under non-smooth convex regularization.…
Trajectory optimization is becoming increasingly powerful in addressing motion planning problems of underactuated robotic systems. Numerous prior studies solve such a class of large non-convex optimal control problems in a hierarchical…
In this paper, we consider minimizing the L1/L2 term on the gradient for a limited-angle scanning problem in computed tomography (CT) reconstruction. We design a specific splitting framework for an unconstrained optimization model so that…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows to…
In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with general convex penalty term. When the data is given exactly, we give a…
Many machine learning models, including those with non-smooth regularizers, can be formulated as consensus optimization problems, which can be solved by the alternating direction method of multipliers (ADMM). Many recent efforts have been…
We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to…
Mathematical modelling, particularly through approaches such as structured sparse support vector machines (SS-SVM), plays a crucial role in processing data with complex feature structures, yet efficient algorithms for distributed…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
As an extension of the alternating direction method of multipliers (ADMM), the semi-proximal ADMM (sPADMM) has been widely used in various fields due to its flexibility and robustness. In this paper, we first show that the two-block sPADMM…
With the recent proliferation of large-scale learning problems,there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However,…
In the context of large-angle cone-beam tomography (CBCT), we present a practical iterative reconstruction (IR) scheme designed for rapid convergence as required for large datasets. The robustness of the reconstruction is provided by the…
Using inverse planning tools to create radiotherapy treatment plans is an iterative process, where clinical trade-offs are explored by changing the relative importance of different objectives and rerunning the optimizer until a desirable…
We propose a state-of-the-art method for super-resolution with non-uniform blur. Single-image super-resolution methods seek to restore a high-resolution image from blurred, subsampled, and noisy measurements. Despite their impressive…
The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and…
In the past decade, sparsity-driven regularization has led to advancement of image reconstruction algorithms. Traditionally, such regularizers rely on analytical models of sparsity (e.g. total variation (TV)). However, more recent methods…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
We present an algorithm to parallelize the inverse fast multipole method (IFMM), which is an approximate direct solver for dense linear systems. The parallel scheme is based on a greedy coloring algorithm, where two nodes in the hierarchy…